2011, Chapman & Hall/CRC monographs and surveys in pure and applied mathematics, ISBN 9781420066548, Volume 143, xiv, 321

Book

Monthly Notices of the Royal Astronomical Society, ISSN 0035-8711, 2017, Volume 467, Issue 2, pp. 1449 - 1477

.... To this end, we compile a large sample of 39 cool core clusters and determine steady state solutions of the hydrodynamic equations that are coupled to the CR energy equation...

Galaxies: clusters: general | Radiation mechanisms: non-thermal | Conduction | Galaxies: active | Cosmic rays | radiation mechanisms: non-thermal | galaxies: clusters: general | MAGNETIC-FIELDS | ELLIPTIC GALAXIES | COLD GAS | GALAXY CLUSTERS | THERMAL CONDUCTION | AGN FEEDBACK | cosmic rays | ACTIVE GALACTIC NUCLEI | STABILITY ANALYSIS | galaxies: active | INTRACLUSTER MEDIUM | ASTRONOMY & ASTROPHYSICS | conduction | X-RAY

Galaxies: clusters: general | Radiation mechanisms: non-thermal | Conduction | Galaxies: active | Cosmic rays | radiation mechanisms: non-thermal | galaxies: clusters: general | MAGNETIC-FIELDS | ELLIPTIC GALAXIES | COLD GAS | GALAXY CLUSTERS | THERMAL CONDUCTION | AGN FEEDBACK | cosmic rays | ACTIVE GALACTIC NUCLEI | STABILITY ANALYSIS | galaxies: active | INTRACLUSTER MEDIUM | ASTRONOMY & ASTROPHYSICS | conduction | X-RAY

Journal Article

Results in Mathematics, ISSN 1422-6383, 6/2019, Volume 74, Issue 2, pp. 1 - 34

.... We produce three nontrivial solutions for small values of the parameter. We provide sign information for all solutions...

constant sign and nodal solutions | 35J20 | 58E05 | 35J60 | critical groups | 35J92 | Competing nonlinearities | concave term | Mathematics, general | multiplicity theorems | Mathematics | resonance | MATHEMATICS, APPLIED | MATHEMATICS | NODAL SOLUTIONS | NONLINEAR ELLIPTIC-EQUATIONS | GROWTH | CONSTANT SIGN | Q)-EQUATIONS | Computer science

constant sign and nodal solutions | 35J20 | 58E05 | 35J60 | critical groups | 35J92 | Competing nonlinearities | concave term | Mathematics, general | multiplicity theorems | Mathematics | resonance | MATHEMATICS, APPLIED | MATHEMATICS | NODAL SOLUTIONS | NONLINEAR ELLIPTIC-EQUATIONS | GROWTH | CONSTANT SIGN | Q)-EQUATIONS | Computer science

Journal Article

Communications on pure and applied mathematics, ISSN 1097-0312, 2006, Volume 59, Issue 3, pp. 330 - 343

... -y|^{n-\alpha}}u(y)^{{n+\alpha} \over {n-\alpha}} dy.$$ We prove that every positive regular solution u(x...

SYSTEM | MATHEMATICS | MATHEMATICS, APPLIED | ASYMPTOTIC SYMMETRY | NONLINEAR ELLIPTIC-EQUATIONS | SOBOLEV

SYSTEM | MATHEMATICS | MATHEMATICS, APPLIED | ASYMPTOTIC SYMMETRY | NONLINEAR ELLIPTIC-EQUATIONS | SOBOLEV

Journal Article

Nonlinear dynamics, ISSN 1573-269X, 2018, Volume 95, Issue 1, pp. 273 - 291

.... By considering the consistent tanh expansion method, the interaction solution of soliton-cnoidal wave for the classical BB equation is studied by using the Jacobi elliptic function...

Conservation laws | Lie point symmetry | The classical Boussinesq–Burgers equation | Interaction solutions | Truncated painlevé expansion | EVOLUTION-EQUATIONS | PERIODIC-WAVE SOLUTIONS | ENGINEERING, MECHANICAL | ROGUE WAVES | BACKLUND TRANSFORMATION | BOUNDARY VALUE-PROBLEMS | MECHANICS | SOLITONS | SOLITARY WAVES | Truncated painleve expansion | DYNAMICS | The classical Boussinesq-Burgers equation | HOMOCLINIC BREATHER WAVES | DARBOUX TRANSFORMATIONS | Water waves | Laws, regulations and rules | Environmental law | Wave propagation | Boussinesq equations | Dependent variables | Cnoidal waves | Exponential functions | Elliptic functions | Burgers equation | Shallow water | Solitary waves | Symmetry

Conservation laws | Lie point symmetry | The classical Boussinesq–Burgers equation | Interaction solutions | Truncated painlevé expansion | EVOLUTION-EQUATIONS | PERIODIC-WAVE SOLUTIONS | ENGINEERING, MECHANICAL | ROGUE WAVES | BACKLUND TRANSFORMATION | BOUNDARY VALUE-PROBLEMS | MECHANICS | SOLITONS | SOLITARY WAVES | Truncated painleve expansion | DYNAMICS | The classical Boussinesq-Burgers equation | HOMOCLINIC BREATHER WAVES | DARBOUX TRANSFORMATIONS | Water waves | Laws, regulations and rules | Environmental law | Wave propagation | Boussinesq equations | Dependent variables | Cnoidal waves | Exponential functions | Elliptic functions | Burgers equation | Shallow water | Solitary waves | Symmetry

Journal Article

Superlattices and Microstructures, ISSN 0749-6036, 01/2018, Volume 113, pp. 510 - 518

In this paper, we consider the cubic Schrödinger equation with a bounded potential, which describes the propagation properties of optical soliton solutions...

Dark soliton solutions | Bright soliton solutions | Jacobi's elliptic function | Complexitons | The cubic Schrödinger equation | Analytic periodic wave solution | PHYSICS, CONDENSED MATTER | NONLINEAR DISPERSIVE WAVES | FLUID-DYNAMICS | The cubic Schrodinger equation | HIROTA EQUATION | KADOMTSEV-PETVIASHVILI EQUATION | ROGUE WAVES | SYMBOLIC COMPUTATION | (2+1)-DIMENSIONAL ITO EQUATION | BURGERS-EQUATION | CONSERVATION-LAWS | RATIONAL CHARACTERISTICS

Dark soliton solutions | Bright soliton solutions | Jacobi's elliptic function | Complexitons | The cubic Schrödinger equation | Analytic periodic wave solution | PHYSICS, CONDENSED MATTER | NONLINEAR DISPERSIVE WAVES | FLUID-DYNAMICS | The cubic Schrodinger equation | HIROTA EQUATION | KADOMTSEV-PETVIASHVILI EQUATION | ROGUE WAVES | SYMBOLIC COMPUTATION | (2+1)-DIMENSIONAL ITO EQUATION | BURGERS-EQUATION | CONSERVATION-LAWS | RATIONAL CHARACTERISTICS

Journal Article

Journal of physics. A, Mathematical and theoretical, ISSN 1751-8121, 2019, Volume 52, Issue 46, p. 465201

We point out novel connections between complex PT-invariant solutions of several nonlinear equations such as phi(4), phi(6...

nonlinear equations | kink solutions | PT-symmetry | PHYSICS, MULTIDISCIPLINARY | MODEL | PHYSICS, MATHEMATICAL | elliptic functions

nonlinear equations | kink solutions | PT-symmetry | PHYSICS, MULTIDISCIPLINARY | MODEL | PHYSICS, MATHEMATICAL | elliptic functions

Journal Article

Journal of Dynamics and Differential Equations, ISSN 1040-7294, 3/2019, Volume 31, Issue 1, pp. 369 - 383

.... G for some domain G. RN to show the existence of nontrivial solutions for the above problem.

35J20 | Local super-quadratic conditions | Ordinary Differential Equations | 35J60 | Mathematics | Superlinear | Applications of Mathematics | Partial Differential Equations | Schrödinger equation | Asymptotically linear | MATHEMATICS | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | Schrodinger equation | GROUND-STATES

35J20 | Local super-quadratic conditions | Ordinary Differential Equations | 35J60 | Mathematics | Superlinear | Applications of Mathematics | Partial Differential Equations | Schrödinger equation | Asymptotically linear | MATHEMATICS | ELLIPTIC PROBLEMS | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | Schrodinger equation | GROUND-STATES

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2012, Volume 252, Issue 3, pp. 2544 - 2562

.... the nonexistence of positive solutions in the whole space R N . It has been conjectured that this property is true if (and only if) p < p S ( a ) , where p S ( a ) is...

Liouville-type theorem | Decay estimate | Nonexistence | A priori estimates | Hardy–Hénon equation | Universal bounds | Isolated singularity | Nonlinear elliptic equation | Secondary | Primary | Hardy-Hénon equation | POSITIVE SOLUTIONS | GROUND-STATE SOLUTIONS | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | PROFILE | Hardy-Henon equation | ELLIPTIC-EQUATIONS

Liouville-type theorem | Decay estimate | Nonexistence | A priori estimates | Hardy–Hénon equation | Universal bounds | Isolated singularity | Nonlinear elliptic equation | Secondary | Primary | Hardy-Hénon equation | POSITIVE SOLUTIONS | GROUND-STATE SOLUTIONS | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | PROFILE | Hardy-Henon equation | ELLIPTIC-EQUATIONS

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 02/2017, Volume 73, Issue 3, pp. 505 - 519

In this paper, we prove the existence of positive solutions and negative solutions for the following modified Schrödinger–Kirchhoff...

Modified Schrödinger–Kirchhoff–Poisson system | Nontrivial nonnegative solutions | Perturbation methods | High energy solutions | Nontrivial nonpositive solutions | MATHEMATICS, APPLIED | NONTRIVIAL SOLUTION | P-LAPLACIAN EQUATIONS | LINEAR ELLIPTIC-EQUATIONS | POSITIVE SOLUTIONS | Modified Schrodinger-Kirchhoff-Poisson system | Energy industry | Methods

Modified Schrödinger–Kirchhoff–Poisson system | Nontrivial nonnegative solutions | Perturbation methods | High energy solutions | Nontrivial nonpositive solutions | MATHEMATICS, APPLIED | NONTRIVIAL SOLUTION | P-LAPLACIAN EQUATIONS | LINEAR ELLIPTIC-EQUATIONS | POSITIVE SOLUTIONS | Modified Schrodinger-Kirchhoff-Poisson system | Energy industry | Methods

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 10/2015, Volume 259, Issue 8, pp. 3894 - 3928

In this paper we prove the existence of two solutions having a prescribed L2-norm for a quasi-linear Schrödinger equation...

[formula omitted]-normalized solutions | Perturbation method | Liouville type results | Quasi-linear Schrödinger equations | normalized solutions | EXISTENCE | SCALAR FIELD-EQUATIONS | INSTABILITY | POISSON | STANDING WAVES | MATHEMATICS | Quasi-linear Schrodinger equations | SOLITON-SOLUTIONS | PRESCRIBED NORM | L-2-normalized solutions | ELLIPTIC-EQUATIONS | GROUND-STATES | Analysis of PDEs | Mathematics

[formula omitted]-normalized solutions | Perturbation method | Liouville type results | Quasi-linear Schrödinger equations | normalized solutions | EXISTENCE | SCALAR FIELD-EQUATIONS | INSTABILITY | POISSON | STANDING WAVES | MATHEMATICS | Quasi-linear Schrodinger equations | SOLITON-SOLUTIONS | PRESCRIBED NORM | L-2-normalized solutions | ELLIPTIC-EQUATIONS | GROUND-STATES | Analysis of PDEs | Mathematics

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2010, Volume 248, Issue 4, pp. 722 - 744

In this paper we establish the existence of standing wave solutions for quasilinear...

Critical exponent | Variational methods | Minimax methods | Schrödinger equations | Standing wave solutions | EXISTENCE | SCALAR FIELD-EQUATIONS | POSITIVE SOLUTIONS | MATHEMATICS | R-N | WAVES | Schrodinger equations | PLASMA | ELLIPTIC-EQUATIONS

Critical exponent | Variational methods | Minimax methods | Schrödinger equations | Standing wave solutions | EXISTENCE | SCALAR FIELD-EQUATIONS | POSITIVE SOLUTIONS | MATHEMATICS | R-N | WAVES | Schrodinger equations | PLASMA | ELLIPTIC-EQUATIONS

Journal Article

Archive for rational mechanics and analysis, ISSN 1432-0673, 2009, Volume 195, Issue 2, pp. 455 - 467

In this paper, we settle the longstanding open problem concerning the classification of all positive solutions to the nonlinear stationary Choquard equation $$\Delta u-u+2u\left(\frac{1}{|x|}*|u|^2\right)=0, \quad u\in H^1(\mathbb{R}^3...

Elliptic System | Sobolev Inequality | Fluid- and Aerodynamics | Integral Equation | Theoretical, Mathematical and Computational Physics | Complex Systems | Classical Mechanics | Physics, general | Uniqueness Result | Nonlinear Elliptic Equation | Physics | SCHRODINGER-EQUATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | RADIAL SYMMETRY | BOUND-STATES | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | INTEGRAL-EQUATIONS | SYSTEMS | UNIQUENESS

Elliptic System | Sobolev Inequality | Fluid- and Aerodynamics | Integral Equation | Theoretical, Mathematical and Computational Physics | Complex Systems | Classical Mechanics | Physics, general | Uniqueness Result | Nonlinear Elliptic Equation | Physics | SCHRODINGER-EQUATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | RADIAL SYMMETRY | BOUND-STATES | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | INTEGRAL-EQUATIONS | SYSTEMS | UNIQUENESS

Journal Article

2015, CBMS-NSF regional conference series in applied mathematics, ISBN 9781611973778, Volume 86., xix, 462

Variational Methods for the Numerical Solution of Nonlinear Elliptic Problems addresses computational methods that have proven efficient for the solution of a large variety of nonlinear elliptic problems...

Eikonal equation | Elliptic functions | Nonlinear functional analysis | Lagrangian functions

Eikonal equation | Elliptic functions | Nonlinear functional analysis | Lagrangian functions

Book

International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 12/2014, Volume 76, Issue 11, pp. 855 - 874

.... The nonlinear system of algebraic equations with unknowns the intermediate solutions of the Runge...

Newton–Picard iterative methods | (p,δ)‐structure system of equations | numerical solutions in domains with non‐smooth boundary | (p,δ)‐structure penalty jump terms | local discontinuous Galerkin methods | (p,δ)-structure system of equations | Newton-Picard iterative methods | (p,δ)-structure penalty jump terms | Numerical solutions in domains with non-smooth boundary | Local discontinuous Galerkin methods | APPROXIMATION | structure system of equations | PHYSICS, FLUIDS & PLASMAS | UNIFIED ANALYSIS | NONLINEAR DIFFUSION-PROBLEMS | ELLIPTIC PROBLEMS | ORDER | P-LAPLACIAN | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | structure penalty jump terms | MESH REFINEMENT | numerical solutions in domains with non-smooth boundary | Mathematical analysis | Nonlinearity | Mathematical models | Runge-Kutta method | Boundaries | Fluxes | Iterative methods | Galerkin methods

Newton–Picard iterative methods | (p,δ)‐structure system of equations | numerical solutions in domains with non‐smooth boundary | (p,δ)‐structure penalty jump terms | local discontinuous Galerkin methods | (p,δ)-structure system of equations | Newton-Picard iterative methods | (p,δ)-structure penalty jump terms | Numerical solutions in domains with non-smooth boundary | Local discontinuous Galerkin methods | APPROXIMATION | structure system of equations | PHYSICS, FLUIDS & PLASMAS | UNIFIED ANALYSIS | NONLINEAR DIFFUSION-PROBLEMS | ELLIPTIC PROBLEMS | ORDER | P-LAPLACIAN | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | NAVIER-STOKES EQUATIONS | structure penalty jump terms | MESH REFINEMENT | numerical solutions in domains with non-smooth boundary | Mathematical analysis | Nonlinearity | Mathematical models | Runge-Kutta method | Boundaries | Fluxes | Iterative methods | Galerkin methods

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2006, Volume 229, Issue 2, pp. 743 - 767

Existence of a nontrivial solution is established, via variational methods, for a system of weakly coupled nonlinear Schrödinger equations...

Least energy solution | Nonlinear elliptic system | Weakly coupled Schrödinger equations | EXISTENCE | PRINCIPLE | nonlinear elliptic system | UNIQUENESS | MATHEMATICS | R-N | weakly coupled Schrodinger equations | SOLITARY WAVES | least energy solution | FIELD-EQUATIONS | OPTICAL FIBERS | SEMILINEAR ELLIPTIC EQUATION | GROUND-STATES | BIFURCATION

Least energy solution | Nonlinear elliptic system | Weakly coupled Schrödinger equations | EXISTENCE | PRINCIPLE | nonlinear elliptic system | UNIQUENESS | MATHEMATICS | R-N | weakly coupled Schrodinger equations | SOLITARY WAVES | least energy solution | FIELD-EQUATIONS | OPTICAL FIBERS | SEMILINEAR ELLIPTIC EQUATION | GROUND-STATES | BIFURCATION

Journal Article

Communications on Pure and Applied Mathematics, ISSN 0010-3640, 04/2020, Volume 73, Issue 4, pp. 771 - 854

We study the one‐dimensional symmetry of solutions to the nonlinear Stokes equation {−Δu+∇W(u)=∇pin ℝd,∇⋅u=0in...

COMPACTNESS RESULT | MATHEMATICS | MATHEMATICS, APPLIED | UPPER-BOUNDS | ENERGY | SINGULAR PERTURBATION | SYMMETRY | DOMAIN-WALLS | NEEL | DE-GIORGI | HETEROCLINIC CONNECTION PROBLEM | ELLIPTIC SYSTEM | Analysis of PDEs | Mathematics

COMPACTNESS RESULT | MATHEMATICS | MATHEMATICS, APPLIED | UPPER-BOUNDS | ENERGY | SINGULAR PERTURBATION | SYMMETRY | DOMAIN-WALLS | NEEL | DE-GIORGI | HETEROCLINIC CONNECTION PROBLEM | ELLIPTIC SYSTEM | Analysis of PDEs | Mathematics

Journal Article