Nonlinear Analysis, ISSN 0362-546X, 2012, Volume 75, Issue 3, pp. 1524 - 1530

We are concerned with the Lane–Emden–Fowler equation − Δ u = λ k ( x ) u q ± h ( x ) u p in Ω , subject to the Dirichlet boundary condition u = 0 on ∂ Ω ,...

Anisotropic continuous media | Lane–Emden–Fowler equation | Perturbation | Bifurcation problem | Positive solution | LaneEmdenFowler equation | EXISTENCE | CONVEX NONLINEARITIES | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | Lane-Emden-Fowler equation | NONEXISTENCE | FIBERING METHOD | MATHEMATICS | CONCAVE | ELLIPTIC-EQUATIONS | ASYMPTOTICALLY LINEAR FUNCTION | Media | Boundary conditions | Dirichlet problem | Nonlinearity | Anisotropy | Mathematical analysis | Mathematics - Analysis of PDEs

Anisotropic continuous media | Lane–Emden–Fowler equation | Perturbation | Bifurcation problem | Positive solution | LaneEmdenFowler equation | EXISTENCE | CONVEX NONLINEARITIES | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | Lane-Emden-Fowler equation | NONEXISTENCE | FIBERING METHOD | MATHEMATICS | CONCAVE | ELLIPTIC-EQUATIONS | ASYMPTOTICALLY LINEAR FUNCTION | Media | Boundary conditions | Dirichlet problem | Nonlinearity | Anisotropy | Mathematical analysis | Mathematics - Analysis of PDEs

Journal Article

Neurocomputing, ISSN 0925-2312, 02/2015, Volume 149, pp. 975 - 982

In this investigation, a new algorithm has been proposed to solve singular initial value problems of Emden–Fowler type equations. Approximate solutions of...

Feed forward model | Chebyshev Neural Network | Error back propagation | Singular initial value problem | Emden–Fowler equation | Emden-Fowler equation | IVPS | DECOMPOSITION METHOD | ALGORITHM | BOUNDARY-VALUE-PROBLEMS | ORDINARY DIFFERENTIAL-EQUATIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | SYSTEM-IDENTIFICATION | Neural networks | Methods | Algorithms

Feed forward model | Chebyshev Neural Network | Error back propagation | Singular initial value problem | Emden–Fowler equation | Emden-Fowler equation | IVPS | DECOMPOSITION METHOD | ALGORITHM | BOUNDARY-VALUE-PROBLEMS | ORDINARY DIFFERENTIAL-EQUATIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | SYSTEM-IDENTIFICATION | Neural networks | Methods | Algorithms

Journal Article

Computer Physics Communications, ISSN 0010-4655, 04/2014, Volume 185, Issue 4, pp. 1282 - 1289

In this work, a new technique based on Green’s function and the Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems...

Nonlinear singular boundary value problem | Modified Adomian decomposition method | Green’s function | Series solutions | Adomian decomposition method | Emden–Fowler equation | Emden-Fowler equation | Green's function | PHYSIOLOGY | ALGORITHM | LANE-EMDEN EQUATIONS | FINITE-DIFFERENCE METHOD | PHYSICS, MATHEMATICAL | POLYNOMIALS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONVERGENCE | SPLINE

Nonlinear singular boundary value problem | Modified Adomian decomposition method | Green’s function | Series solutions | Adomian decomposition method | Emden–Fowler equation | Emden-Fowler equation | Green's function | PHYSIOLOGY | ALGORITHM | LANE-EMDEN EQUATIONS | FINITE-DIFFERENCE METHOD | PHYSICS, MATHEMATICAL | POLYNOMIALS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONVERGENCE | SPLINE

Journal Article

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, ISSN 0294-1449, Volume 9, Issue 4, pp. 367 - 397

For the Emden-Fowler equation −Δu=λe in Ω ⊂ R , the connectivity of the trivial solution and the one-point blow-up singular limit is studied with respect to...

Emden-Fowler equation | global bifurcation | singular limit | rearrangement

Emden-Fowler equation | global bifurcation | singular limit | rearrangement

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2006, Volume 231, Issue 1, pp. 18 - 31

In this paper, some sufficient conditions for the existence of solutions to the boundary value problems of a class of second order difference equation are...

Boundary value problem | Difference equation | Emden–Fowler equation | Saddle point theorem | Emden-Fowler equation | difference equation | EXISTENCE | SUBHARMONIC SOLUTIONS | POSITIVE SOLUTIONS | DIFFERENCE-EQUATIONS | OSCILLATION | MATHEMATICS | DISCONJUGACY | GROWTH | SYSTEMS | boundary value problem

Boundary value problem | Difference equation | Emden–Fowler equation | Saddle point theorem | Emden-Fowler equation | difference equation | EXISTENCE | SUBHARMONIC SOLUTIONS | POSITIVE SOLUTIONS | DIFFERENCE-EQUATIONS | OSCILLATION | MATHEMATICS | DISCONJUGACY | GROWTH | SYSTEMS | boundary value problem

Journal Article

Computational Mathematics and Mathematical Physics, ISSN 0965-5425, 8/2019, Volume 59, Issue 8, pp. 1292 - 1313

A two-point boundary value problem is considered for the Emden–Fowler equation, which is a singular nonlinear ordinary differential equation of the second...

Computational Mathematics and Numerical Analysis | Painlevé test | Emden–Fowler equation | Mathematics | Abel equation of the second kind | Fuchs index | Thomas–Fermi problem | parametric representation | Painleve test | MATHEMATICS, APPLIED | Emden-Fowler equation | Thomas-Fermi problem | ABEL | EXACT ANALYTIC SOLUTIONS | MODEL | PHYSICS, MATHEMATICAL | CHEBYSHEV SERIES | Computer science | Algorithms | Differential equations | Charged ions | Boundary value problems | Representations

Computational Mathematics and Numerical Analysis | Painlevé test | Emden–Fowler equation | Mathematics | Abel equation of the second kind | Fuchs index | Thomas–Fermi problem | parametric representation | Painleve test | MATHEMATICS, APPLIED | Emden-Fowler equation | Thomas-Fermi problem | ABEL | EXACT ANALYTIC SOLUTIONS | MODEL | PHYSICS, MATHEMATICAL | CHEBYSHEV SERIES | Computer science | Algorithms | Differential equations | Charged ions | Boundary value problems | Representations

Journal Article

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Exact boundary behavior of the unique positive solution to some singular elliptic problems

Nonlinear Analysis, ISSN 0362-546X, 09/2013, Volume 89, pp. 146 - 156

In this paper, we give an exact asymptotic of the unique solution to the following singular boundary value problem −Δu=a(x)g(u),x∈Ω,u>0, in Ω,u|∂Ω=0. Here Ω...

Semilinear elliptic equations | Singular Dirichlet problem | The boundary behavior | Singular | Dirichlet problem | MATHEMATICS | MATHEMATICS, APPLIED | EMDEN-FOWLER EQUATION | DIRICHLET PROBLEM | ASYMPTOTIC-BEHAVIOR

Semilinear elliptic equations | Singular Dirichlet problem | The boundary behavior | Singular | Dirichlet problem | MATHEMATICS | MATHEMATICS, APPLIED | EMDEN-FOWLER EQUATION | DIRICHLET PROBLEM | ASYMPTOTIC-BEHAVIOR

Journal Article

Bulletin des sciences mathématiques, ISSN 0007-4497, 10/2014, Volume 138, Issue 7, pp. 846 - 859

In this work we obtain existence results for some singular elliptic Dirichlet problems involving the p-Laplacian. Precisely, starting from a weak lower...

MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | EMDEN-FOWLER EQUATION | POSITIVE SOLUTIONS

MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | EMDEN-FOWLER EQUATION | POSITIVE SOLUTIONS

Journal Article

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Control of error in the homotopy analysis of nonlinear Klein–Gordon initial value problems

Applied Mathematics and Computation, ISSN 0096-3003, 02/2013, Volume 219, Issue 12, pp. 6494 - 6509

In the present paper, we discuss the application of homotopy analysis to general nonlinear Klein–Gordon type equations. We first outline the method for general...

sinh-Gordon equation | tanh-Gordon equation | Control of error | Quasilinear Klein–Gordon equation | Homotopy analysis method | Quasilinear Klein-Gordon equation | EXPANSION METHOD | MATHEMATICS, APPLIED | EQUATIONS | FLOW | WAVES | SINH-GORDON | EVOLUTION | FLUID | EMDEN-FOWLER TYPE | ASYMPTOTIC METHOD

sinh-Gordon equation | tanh-Gordon equation | Control of error | Quasilinear Klein–Gordon equation | Homotopy analysis method | Quasilinear Klein-Gordon equation | EXPANSION METHOD | MATHEMATICS, APPLIED | EQUATIONS | FLOW | WAVES | SINH-GORDON | EVOLUTION | FLUID | EMDEN-FOWLER TYPE | ASYMPTOTIC METHOD

Journal Article

Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 2011, Volume 12, Issue 5, pp. 2656 - 2665

The existence of three nontrivial solutions for a nonlinear problem on compact d -dimensional ( d ≥ 3 ) Riemannian manifolds without boundary, is established....

Multiple solutions | Yamabe problem | Emden–Fowler equation | Sublinear eigenvalue problem | MATHEMATICS, APPLIED | Emden-Fowler equation | Concretes | Manifolds | Infinity | Thermionic emission | Mathematical analysis | Nonlinearity | Combustion | Boundaries

Multiple solutions | Yamabe problem | Emden–Fowler equation | Sublinear eigenvalue problem | MATHEMATICS, APPLIED | Emden-Fowler equation | Concretes | Manifolds | Infinity | Thermionic emission | Mathematical analysis | Nonlinearity | Combustion | Boundaries

Journal Article

Journal of Mathematical Chemistry, ISSN 0259-9791, 10/2015, Volume 53, Issue 9, pp. 2095 - 2113

In this paper, we have established an efficient wavelet based approximation method to nonlinear singular boundary value problems. To the best of our knowledge,...

Theoretical and Computational Chemistry | Chemistry | Physical Chemistry | Chebyshev wavelets | Singular boundary value problems | Operational matrices | Math. Applications in Chemistry | Emden–Fowler equations | OPERATIONAL MATRIX | NUMERICAL-SOLUTION | PHYSIOLOGY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | HAAR WAVELET | DIFFERENTIAL-EQUATIONS | Emden-Fowler equations | DIFFUSION | CHEMISTRY, MULTIDISCIPLINARY | Wavelet transforms | Boundary value problems | Differential equations, Nonlinear | Analysis

Theoretical and Computational Chemistry | Chemistry | Physical Chemistry | Chebyshev wavelets | Singular boundary value problems | Operational matrices | Math. Applications in Chemistry | Emden–Fowler equations | OPERATIONAL MATRIX | NUMERICAL-SOLUTION | PHYSIOLOGY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | HAAR WAVELET | DIFFERENTIAL-EQUATIONS | Emden-Fowler equations | DIFFUSION | CHEMISTRY, MULTIDISCIPLINARY | Wavelet transforms | Boundary value problems | Differential equations, Nonlinear | Analysis

Journal Article

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A Multiplicity Result for a Class of Elliptic Problems on a Compact Riemannian Manifold

Journal of Optimization Theory and Applications, ISSN 0022-3239, 12/2015, Volume 167, Issue 3, pp. 912 - 927

The existence of multiple solutions for a constrained eigenvalue problem on a compact Riemannian manifold without boundary is proved. In the framework of...

Multiple solutions | Analysis on manifolds | Calculus of Variations and Optimal Control; Optimization | Critical points | Mathematics | Theory of Computation | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | Emden–Fowler problems | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CRITICAL-POINT THEORY | GROWTH | MOUNTAIN PASS THEOREM | EQUATIONS | Emden-Fowler problems | Computer science | Analysis | Studies | Topological manifolds | Mathematical analysis | Eigen values | Manifolds | Constraints | Eigenvalues | Critical point | Boundaries

Multiple solutions | Analysis on manifolds | Calculus of Variations and Optimal Control; Optimization | Critical points | Mathematics | Theory of Computation | Applications of Mathematics | Engineering, general | Operation Research/Decision Theory | Emden–Fowler problems | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CRITICAL-POINT THEORY | GROWTH | MOUNTAIN PASS THEOREM | EQUATIONS | Emden-Fowler problems | Computer science | Analysis | Studies | Topological manifolds | Mathematical analysis | Eigen values | Manifolds | Constraints | Eigenvalues | Critical point | Boundaries

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 08/2016, Volume 39, Issue 12, pp. 3204 - 3214

In the manuscript, a pseudospectral method is developed for approximate and efficient solution of nonlinear singular Lane–Emden–Fowler initial and boundary...

Legendre–Gauss points | Lane–Emden–Fowler equation | Gauss pseudospectral method | boundary singularity | VARIATIONAL ITERATION METHOD | MATHEMATICS, APPLIED | Lane-Emden-Fowler equation | EMDEN TYPE EQUATIONS | ALGORITHM | Legendre-Gauss points | Boundary value problems | Approximation | Astrophysics | Mathematical analysis | Stars | Nonlinearity | Mathematical models | Convergence

Legendre–Gauss points | Lane–Emden–Fowler equation | Gauss pseudospectral method | boundary singularity | VARIATIONAL ITERATION METHOD | MATHEMATICS, APPLIED | Lane-Emden-Fowler equation | EMDEN TYPE EQUATIONS | ALGORITHM | Legendre-Gauss points | Boundary value problems | Approximation | Astrophysics | Mathematical analysis | Stars | Nonlinearity | Mathematical models | Convergence

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 05/2013, Volume 244, Issue 1, pp. 125 - 139

In this paper a class of Birkhoff-type interpolation problems on arbitrary nodal points is studied. The explicit representation (characterization), the...

Initial value problems | Quadrature rules | Error analysis | Special functions | Birkhoff interpolation | MATHEMATICS, APPLIED | ALGORITHM | BOUNDARY-VALUE-PROBLEMS | DIFFERENTIAL-EQUATIONS | INTEGRATION | CONVERGENCE | SYSTEMS | EMDEN-FOWLER EQUATIONS | Interpolation | Approximation | Mathematical analysis | Uniqueness | Error functions | Mathematical models | Representations

Initial value problems | Quadrature rules | Error analysis | Special functions | Birkhoff interpolation | MATHEMATICS, APPLIED | ALGORITHM | BOUNDARY-VALUE-PROBLEMS | DIFFERENTIAL-EQUATIONS | INTEGRATION | CONVERGENCE | SYSTEMS | EMDEN-FOWLER EQUATIONS | Interpolation | Approximation | Mathematical analysis | Uniqueness | Error functions | Mathematical models | Representations

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 03/2015, Volume 38, Issue 5, pp. 980 - 990

In this paper, we consider a class of second‐order initial value problems. We extend the family of second‐order initial value problems for which the existence...

Lane–Emden equation | existence | IVPs | Emden–Fowler equation | Caratheodory conditions | Emden-Fowler equation | Lane-Emden equation | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | ALGORITHM | BOUNDARY-VALUE-PROBLEMS | APPROXIMATE SOLUTION | FOWLER EQUATION | ORDINARY DIFFERENTIAL-EQUATIONS | Constrictions | Handles | Initial value problems | Singularities | Mathematical analysis | Uniqueness

Lane–Emden equation | existence | IVPs | Emden–Fowler equation | Caratheodory conditions | Emden-Fowler equation | Lane-Emden equation | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | ALGORITHM | BOUNDARY-VALUE-PROBLEMS | APPROXIMATE SOLUTION | FOWLER EQUATION | ORDINARY DIFFERENTIAL-EQUATIONS | Constrictions | Handles | Initial value problems | Singularities | Mathematical analysis | Uniqueness

Journal Article

Nonlinear Analysis, Theory, Methods and Applications, ISSN 0362-546X, 06/2015, Volume 119, pp. 186 - 198

In this paper, we give an exact behavior on the boundary and at infinity of the unique solution to the following singular boundary value problem...

Singular Dirichlet problem | The asymptotic behavior | Semilinear elliptic equations | Exterior domain | MATHEMATICS | MATHEMATICS, APPLIED | EMDEN-FOWLER EQUATION | DIRICHLET PROBLEM | ASYMPTOTIC-BEHAVIOR | BOUNDARY-BEHAVIOR | Boundary value problems | Infinity | Mathematical analysis | Exteriors | Texts | Nonlinearity | Boundaries

Singular Dirichlet problem | The asymptotic behavior | Semilinear elliptic equations | Exterior domain | MATHEMATICS | MATHEMATICS, APPLIED | EMDEN-FOWLER EQUATION | DIRICHLET PROBLEM | ASYMPTOTIC-BEHAVIOR | BOUNDARY-BEHAVIOR | Boundary value problems | Infinity | Mathematical analysis | Exteriors | Texts | Nonlinearity | Boundaries

Journal Article

Physica Scripta, ISSN 1402-4896, 01/2011, Volume 83, Issue 1, p. 015011

In this paper, we propose radial basis functions for solving some well-known classes of astrophysics problems categorized as nonlinear singular initial...

INTERPOLATION | SOLVING DIFFERENTIAL-EQUATIONS | SINGULAR IVPS | NONLINEAR EQUATIONS | PHYSICS, MULTIDISCIPLINARY | ALGORITHM | APPROXIMATE SOLUTION | HOMOTOPY ANALYSIS METHOD | EMDEN-FOWLER EQUATIONS | COLLOCATION

INTERPOLATION | SOLVING DIFFERENTIAL-EQUATIONS | SINGULAR IVPS | NONLINEAR EQUATIONS | PHYSICS, MULTIDISCIPLINARY | ALGORITHM | APPROXIMATE SOLUTION | HOMOTOPY ANALYSIS METHOD | EMDEN-FOWLER EQUATIONS | COLLOCATION

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 9/2016, Volume 110, Issue 2, pp. 385 - 393

In this paper, we establish the existence of at least two distinct weak solutions for some singular elliptic problems involving a p-Laplace operator, subject...

Variational methods | 35J60 | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | p -Laplace operator | Critical point | Applications of Mathematics | 35J35 | Singular problem | p-Laplace operator | MATHEMATICS | MULTIPLE SOLUTIONS | EMDEN-FOWLER EQUATION | BIFURCATION | Dirichlet problem | Texts | Boundary conditions | Operators | Functionals

Variational methods | 35J60 | Theoretical, Mathematical and Computational Physics | Mathematics, general | Mathematics | p -Laplace operator | Critical point | Applications of Mathematics | 35J35 | Singular problem | p-Laplace operator | MATHEMATICS | MULTIPLE SOLUTIONS | EMDEN-FOWLER EQUATION | BIFURCATION | Dirichlet problem | Texts | Boundary conditions | Operators | Functionals

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 03/2015, Volume 38, Issue 4, pp. 691 - 700

This paper is concerned with a class of fourth‐order nonlinear difference equations. By using the critical point theory, we establish various sets of...

discrete variational theory | Dirichlet boundary value problems | nonexistence and existence | fourth‐order | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | ANNULUS | EMDEN-FOWLER EQUATION | POSITIVE SOLUTIONS | BEAM EQUATIONS | fourth-order | Fourth-order | Discrete variational theory | Nonexistence and existence | Boundary value problems | Difference equations | Mathematical analysis | Dirichlet problem | Nonlinearity | Complement | Critical point

discrete variational theory | Dirichlet boundary value problems | nonexistence and existence | fourth‐order | PERIODIC-SOLUTIONS | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | ANNULUS | EMDEN-FOWLER EQUATION | POSITIVE SOLUTIONS | BEAM EQUATIONS | fourth-order | Fourth-order | Discrete variational theory | Nonexistence and existence | Boundary value problems | Difference equations | Mathematical analysis | Dirichlet problem | Nonlinearity | Complement | Critical point

Journal Article