Journal de mathématiques pures et appliquées, ISSN 0021-7824, 01/2017, Volume 107, Issue 1, pp. 41 - 77

In this paper we consider singular semilinear elliptic equations whose prototype is the following{−divA(x)Du=f(x)g(u)+l(x)inΩ,u=0on∂Ω, where Ω...

Homogenization | Singularity at [formula omitted] | Stability | Semilinear equations | Existence | Uniqueness | Singularity at u=0 | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Homogenization | Singularity at [formula omitted] | Stability | Semilinear equations | Existence | Uniqueness | Singularity at u=0 | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 08/2017, Volume 263, Issue 3, pp. 1907 - 1930

We establish quantitative asymptotic behaviors for nonnegative solutions of the critical semilinear equation −Δu=un+2n...

Asymptotic analysis | Boundary isolated singularity | Critical semilinear elliptic equations | MATHEMATICS | LOCAL BEHAVIOR | POSITIVE SOLUTIONS | THEOREMS

Asymptotic analysis | Boundary isolated singularity | Critical semilinear elliptic equations | MATHEMATICS | LOCAL BEHAVIOR | POSITIVE SOLUTIONS | THEOREMS

Journal Article

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Full Text
Nonlocal solutions of parabolic equations with strongly elliptic differential operators

Journal of mathematical analysis and applications, ISSN 0022-247X, 2019, Volume 473, Issue 1, pp. 421 - 443

The paper deals with second order parabolic equations on bounded domains with Dirichlet conditions in arbitrary Euclidean spaces...

Lyapunov-like functions | Parabolic equations | Degree theory | Multipoint and mean value conditions | EXISTENCE | MATHEMATICS, APPLIED | SEMILINEAR EVOLUTION-EQUATIONS | TRANSLATION | KRASNOSELSKII TYPE FORMULA | TRAJECTORIES METHOD | UNIQUENESS | MATHEMATICS | BOUNDARY

Lyapunov-like functions | Parabolic equations | Degree theory | Multipoint and mean value conditions | EXISTENCE | MATHEMATICS, APPLIED | SEMILINEAR EVOLUTION-EQUATIONS | TRANSLATION | KRASNOSELSKII TYPE FORMULA | TRAJECTORIES METHOD | UNIQUENESS | MATHEMATICS | BOUNDARY

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2006, Volume 318, Issue 1, pp. 253 - 270

In this paper, we study the combined effect of concave and convex nonlinearities on the number of positive solutions for semilinear elliptic equations with a sign-changing weight function...

Semilinear elliptic equations | Concave–convex nonlinearities | Nehari manifold | Concave-convex nonlinearities | EXACT MULTIPLICITY | MATHEMATICS | semilinear elliptic equations | MATHEMATICS, APPLIED | concave-convex nonlinearities | POSITIVE SOLUTIONS | PRINCIPLE

Semilinear elliptic equations | Concave–convex nonlinearities | Nehari manifold | Concave-convex nonlinearities | EXACT MULTIPLICITY | MATHEMATICS | semilinear elliptic equations | MATHEMATICS, APPLIED | concave-convex nonlinearities | POSITIVE SOLUTIONS | PRINCIPLE

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2014, Volume 412, Issue 1, pp. 138 - 141

Let u be a classical solution of Dirichlet boundary value problem −Δu=f(x,u) in Ω, where Ω is a bounded and O(k)-invariant domain in RN (1⩽k⩽N) and the...

Classical solution | Qualitative result | Semilinear elliptic equation | Symmetry | MATHEMATICS | MATHEMATICS, APPLIED | PARTIAL SYMMETRY | VARIATIONAL-PROBLEMS | INDEX

Classical solution | Qualitative result | Semilinear elliptic equation | Symmetry | MATHEMATICS | MATHEMATICS, APPLIED | PARTIAL SYMMETRY | VARIATIONAL-PROBLEMS | INDEX

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2018, Volume 265, Issue 11, pp. 6009 - 6035

In this article we deal with different forms of the unique continuation property for second order elliptic equations with nonlinear potentials of sublinear growth...

Carleman estimate | Sublinear potential | Unique continuation | Semilinear equation | MATHEMATICS | COUNTEREXAMPLES | INEQUALITIES | COEFFICIENTS | OPERATORS

Carleman estimate | Sublinear potential | Unique continuation | Semilinear equation | MATHEMATICS | COUNTEREXAMPLES | INEQUALITIES | COEFFICIENTS | OPERATORS

Journal Article

Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 8/2018, Volume 25, Issue 4, pp. 1 - 23

We consider semilinear equation of the form $$-Lu=f(x,u)+\mu $$ -Lu=f(x,u)+μ , where L is the operator corresponding to a transient symmetric regular Dirichlet form $${\mathcal {E}}$$ E , $$\mu $$ μ...

Dirichlet operator | Analysis | Semilinear elliptic equation | Mathematics | Measure data | Primary 35J61 | Secondary 35R06 | FORMS | MATHEMATICS, APPLIED | L1 | SYSTEMS | Computer science | Mathematics - Analysis of PDEs

Dirichlet operator | Analysis | Semilinear elliptic equation | Mathematics | Measure data | Primary 35J61 | Secondary 35R06 | FORMS | MATHEMATICS, APPLIED | L1 | SYSTEMS | Computer science | Mathematics - Analysis of PDEs

Journal Article

Journal de mathématiques pures et appliquées, ISSN 0021-7824, 11/2016, Volume 106, Issue 5, pp. 877 - 904

This paper is concerned with semilinear equations in divergence formdiv(A(x)Du)=f(u), where f:R→[0,∞) is nondecreasing. We introduce a sharp Harnack type...

Harnack inequality | Semilinear equations | Nonhomogeneous equations | Elliptic equations in divergence form | MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY | STRONG MAXIMUM PRINCIPLE | Equality

Harnack inequality | Semilinear equations | Nonhomogeneous equations | Elliptic equations in divergence form | MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY | STRONG MAXIMUM PRINCIPLE | Equality

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 09/2013, Volume 265, Issue 6, pp. 890 - 925

We propose a probabilistic definition of solutions of semilinear elliptic equations with (possibly nonlocal...

Measure data | Backward stochastic differential equation | Semilinear elliptic equation | Dirichlet form | ENTROPY SOLUTIONS | MATHEMATICS | SCHRODINGER-OPERATORS

Measure data | Backward stochastic differential equation | Semilinear elliptic equation | Dirichlet form | ENTROPY SOLUTIONS | MATHEMATICS | SCHRODINGER-OPERATORS

Journal Article

SIAM Journal on Control and Optimization, ISSN 0363-0129, 2014, Volume 52, Issue 1, pp. 339 - 364

Optimal control problems in measure spaces governed by semilinear elliptic equations are considered...

Measure controls | Stability analysis | Sparsity | Optimal control | Semilinear elliptic equation | First and second order optimality conditions | semilinear elliptic equation | MATHEMATICS, APPLIED | first and second order optimality conditions | COST | APPROXIMATION | stability analysis | ERROR ANALYSIS | optimal control | sparsity | measure controls | AUTOMATION & CONTROL SYSTEMS | Nonlinearity | Stability | Mathematical analysis | Regularity | Optimization

Measure controls | Stability analysis | Sparsity | Optimal control | Semilinear elliptic equation | First and second order optimality conditions | semilinear elliptic equation | MATHEMATICS, APPLIED | first and second order optimality conditions | COST | APPROXIMATION | stability analysis | ERROR ANALYSIS | optimal control | sparsity | measure controls | AUTOMATION & CONTROL SYSTEMS | Nonlinearity | Stability | Mathematical analysis | Regularity | Optimization

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 3/2015, Volume 62, Issue 3, pp. 652 - 673

.... These methods were applied to numerically solve semilinear elliptic equation for multiple solutions...

Finite element method | Computational Mathematics and Numerical Analysis | 65N12 | Algorithms | Theoretical, Mathematical and Computational Physics | Semilinear elliptic equation | Appl.Mathematics/Computational Methods of Engineering | Minimax method | 35J91 | Mathematics | 65N30 | Convergence | MATHEMATICS, APPLIED | ALGORITHM | CRITICAL-POINTS | Methods | Minimax technique | Approximation | Discretization | Computation | Mathematical analysis | Saddles | Mathematical models

Finite element method | Computational Mathematics and Numerical Analysis | 65N12 | Algorithms | Theoretical, Mathematical and Computational Physics | Semilinear elliptic equation | Appl.Mathematics/Computational Methods of Engineering | Minimax method | 35J91 | Mathematics | 65N30 | Convergence | MATHEMATICS, APPLIED | ALGORITHM | CRITICAL-POINTS | Methods | Minimax technique | Approximation | Discretization | Computation | Mathematical analysis | Saddles | Mathematical models

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2014, Volume 420, Issue 1, pp. 407 - 434

We consider degenerate parabolic and damped hyperbolic equations involving an operator L, that is X-elliptic with respect to a family of locally Lipschitz continuous vector fields X={X1,…,Xm...

Gradient semigroups | Semilinear degenerate hyperbolic equations | Semilinear degenerate parabolic equations | Global attractors | Sub-elliptic operators | POINCARE INEQUALITY | MATHEMATICS, APPLIED | EXPONENTIAL ATTRACTORS | SPACES | THEOREM | VECTOR-FIELDS | MATHEMATICS | BALLS | HARMONIC-FUNCTIONS

Gradient semigroups | Semilinear degenerate hyperbolic equations | Semilinear degenerate parabolic equations | Global attractors | Sub-elliptic operators | POINCARE INEQUALITY | MATHEMATICS, APPLIED | EXPONENTIAL ATTRACTORS | SPACES | THEOREM | VECTOR-FIELDS | MATHEMATICS | BALLS | HARMONIC-FUNCTIONS

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2019, Volume 266, Issue 1, pp. 833 - 875

...{−Lμu=ϵvp+τin Ω,−Lμv=ϵup˜+τ˜in Ω,u=ν,v=ν˜on ∂Ω, where ϵ=±1, p>0, p˜>0, τ and τ˜ are measures on Ω, ν and ν˜ are measures on ∂Ω. We also deal with elliptic systems where the nonlinearities are more general.

Elliptic systems | Boundary trace | Hardy potential | Semilinear equations | MATHEMATICS | SOURCE-TERM | OPERATORS | BOUNDARY SINGULARITIES

Elliptic systems | Boundary trace | Hardy potential | Semilinear equations | MATHEMATICS | SOURCE-TERM | OPERATORS | BOUNDARY SINGULARITIES

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 02/2017, Volume 272, Issue 3, pp. 929 - 975

In the paper we consider elliptic equations of the form −Au=u−γ⋅μ, where A is the operator associated with a regular symmetric Dirichlet form, μ...

Additive functional | Semilinear elliptic equations | Probabilistic potential theory | Dirichlet form | FORMS | MATHEMATICS | SEMIMARTINGALES | CONVERGENCE | FUNCTIONALS

Additive functional | Semilinear elliptic equations | Probabilistic potential theory | Dirichlet form | FORMS | MATHEMATICS | SEMIMARTINGALES | CONVERGENCE | FUNCTIONALS

Journal Article

Numerical Methods for Partial Differential Equations, ISSN 0749-159X, 11/2017, Volume 33, Issue 6, pp. 2005 - 2022

In this article, we investigate the application of pseudo‐transient‐continuation (PTC) schemes for the numerical solution of semilinear elliptic partial differential equations, with possible singular perturbations...

steady states | semilinear elliptic problems | adaptive pseudo transient continuation method | singularly perturbed problems | adaptive finite element methods | dynamical system | EXISTENCE | MATHEMATICS, APPLIED | ERROR | Analysis | Methods | Differential equations | Finite element method | Boundary value problems | Partial differential equations | Robustness (mathematics) | Mathematical analysis | Galerkin method | Boundary element method

steady states | semilinear elliptic problems | adaptive pseudo transient continuation method | singularly perturbed problems | adaptive finite element methods | dynamical system | EXISTENCE | MATHEMATICS, APPLIED | ERROR | Analysis | Methods | Differential equations | Finite element method | Boundary value problems | Partial differential equations | Robustness (mathematics) | Mathematical analysis | Galerkin method | Boundary element method

Journal Article

Monatshefte für Mathematik, ISSN 1436-5081, 2019, Volume 188, Issue 4, pp. 689 - 702

In the paper we first propose a definition of renormalized solution of semilinear elliptic equation involving operator corresponding to a general (possibly nonlocal...

renormalized solution | 60H30 | Semilinear elliptic equation | measure data | Primary: 35D99 | Dirichlet form and operator | Mathematics, general | Mathematics | Secondary: 35J61 | MATHEMATICS | Computer science | Mathematics - Analysis of PDEs

renormalized solution | 60H30 | Semilinear elliptic equation | measure data | Primary: 35D99 | Dirichlet form and operator | Mathematics, general | Mathematics | Secondary: 35J61 | MATHEMATICS | Computer science | Mathematics - Analysis of PDEs

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 12/2016, Volume 18, Issue 6, p. 1550084

Given Ω a bounded open subset of ℝ N , we consider non-negative solutions to the singular semilinear elliptic equation − Δ u = f u β in H loc 1 ( Ω...

comparison principles | uniqueness of the solutions | Singular semilinear elliptic equations | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | NONLINEARITIES

comparison principles | uniqueness of the solutions | Singular semilinear elliptic equations | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | NONLINEARITIES

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2018, Volume 265, Issue 5, pp. 1962 - 1983

We consider positive singular solutions to semilinear elliptic problems with possibly singular nonlinearity...

Semilinear elliptic equations | Singular solutions | Qualitative properties | MATHEMATICS | MOVING PLANE METHOD | SYMMETRY | EQUATIONS

Semilinear elliptic equations | Singular solutions | Qualitative properties | MATHEMATICS | MOVING PLANE METHOD | SYMMETRY | EQUATIONS

Journal Article

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, ISSN 0363-0129, 2019, Volume 57, Issue 4, pp. 3021 - 3045

We investigate full Lipschitzian and full Holderian stability for a class of control problems governed by semilinear elliptic partial differential equations, where the cost functional, the state...

MATHEMATICS, APPLIED | 2ND-ORDER OPTIMALITY CONDITIONS | semilinear elliptic partial differential equations | PARAMETRIC OPTIMAL-CONTROL | combined second-order subdifferential | full Holderian stability | coderivative | BANG CONTROL-PROBLEMS | LIPSCHITZ STABILITY | full Lipschitzian stability | REGULARIZATION | AUTOMATION & CONTROL SYSTEMS | perturbed control problem

MATHEMATICS, APPLIED | 2ND-ORDER OPTIMALITY CONDITIONS | semilinear elliptic partial differential equations | PARAMETRIC OPTIMAL-CONTROL | combined second-order subdifferential | full Holderian stability | coderivative | BANG CONTROL-PROBLEMS | LIPSCHITZ STABILITY | full Lipschitzian stability | REGULARIZATION | AUTOMATION & CONTROL SYSTEMS | perturbed control problem

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 10/2015, Volume 17, Issue 5, p. 1450050

In this paper, we study the nonexistence of positive solutions for the following elliptic equation $-L_\alpha u = f(u)\quad {\rm in}\ \mathbb {R}^m\, {\times}\, \mathbb {R}^k}, $ where Lαu = Δxu + (α + 1)2|x|2αΔyu, α > 0, (x, y) ∈ ℝm × ℝk...

moving planes | Grushin operator | Liouville type theorem | maximum principle | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | SEMILINEAR EQUATIONS | INTEGRAL-EQUATIONS | CLASSIFICATION | MATHEMATICS | R-N | HEISENBERG-GROUP | SYSTEMS | Operators (mathematics) | Nonlinearity | Theorems | Planes | Integrals | Mathematical analysis

moving planes | Grushin operator | Liouville type theorem | maximum principle | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | SEMILINEAR EQUATIONS | INTEGRAL-EQUATIONS | CLASSIFICATION | MATHEMATICS | R-N | HEISENBERG-GROUP | SYSTEMS | Operators (mathematics) | Nonlinearity | Theorems | Planes | Integrals | Mathematical analysis

Journal Article

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