Semilinear Robin problems resonant at both zero and infinity

2018 ◽  
Vol 30 (1) ◽  
pp. 237-251
Author(s):  
Nikolaos S. Papageorgiou ◽  
Vicenţiu D. Rădulescu
Keyword(s):  
Boundary Condition ◽  
Variational Methods ◽  
Elliptic Problem ◽  
Robin Boundary Condition ◽  
Critical Groups ◽  
Smooth Solutions ◽  
Reaction Term ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Robin Boundary

Abstract We consider a semilinear elliptic problem, driven by the Laplacian with Robin boundary condition. We consider a reaction term which is resonant at {\pm\infty} and at 0. Using variational methods and critical groups, we show that under resonance conditions at {\pm\infty} and at zero the problem has at least two nontrivial smooth solutions.

scholarly journals Multiplicity of solutions for singular semilinear elliptic equations with critical Hardy-Sobolev exponents

2008 ◽  
Vol 2 (2) ◽  
pp. 158-174 ◽  
Author(s):  
Qianqiao Guo ◽  
Pengcheng Niu ◽  
Jingbo Dou
Keyword(s):  
Boundary Condition ◽  
Variational Methods ◽  
Elliptic Problem ◽  
Dirichlet Boundary Condition ◽  
Elliptic Equations ◽  
Dirichlet Boundary ◽  
Nontrivial Solutions ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic

We consider the semilinear elliptic problem with critical Hardy-Sobolev exponents and Dirichlet boundary condition. By using variational methods we obtain the existence and multiplicity of nontrivial solutions and improve the former results.

scholarly journals Existence and Multiplicity of Solutions for Resonant (p,2)-Equations

2018 ◽  
Vol 18 (1) ◽  
pp. 105-129 ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Vicenţiu D. Rădulescu ◽  
Dušan D. Repovš
Keyword(s):  
Variational Methods ◽  
Existence Theorem ◽  
Elliptic Equations ◽  
Smooth Solution ◽  
Critical Groups ◽  
Constant Sign ◽  
Smooth Solutions ◽  
Reaction Term ◽  
Existence And Multiplicity ◽  
Multiplicity Theorem

Abstract We consider Dirichlet elliptic equations driven by the sum of a p-Laplacian {(2<p)} and a Laplacian. The conditions on the reaction term imply that the problem is resonant at both {\pm\infty} and at zero. We prove an existence theorem (producing one nontrivial smooth solution) and a multiplicity theorem (producing five nontrivial smooth solutions, four of constant sign and the fifth nodal; the solutions are ordered). Our approach uses variational methods and critical groups.

scholarly journals A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient Dependence

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 658 ◽  
Author(s):  
Dumitru Motreanu ◽  
Angela Sciammetta ◽  
Elisabetta Tornatore
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Robin Boundary Condition ◽  
Convection Term ◽  
Nonlinear Elliptic Problem ◽  
Existence Of A Solution ◽  
Nonlinear Elliptic ◽  
Robin Boundary

The paper investigates a nonlinear elliptic problem with a Robin boundary condition, which exhibits a convection term with full dependence on the solution and its gradient. A sub- supersolution approach is developed for this type of problems. The main result establishes the existence of a solution enclosed in the ordered interval formed by a sub-supersolution. The result is applied to find positive solutions.

scholarly journals Multiplicity of solutions for Robin problem involving the p(x)-laplacian

2021 ◽  
Vol 13 (2) ◽  
pp. 321-335
Author(s):  
Hassan Belaouidel ◽  
Anass Ourraoui ◽  
Najib Tsouli
Keyword(s):  
Boundary Condition ◽  
Variational Methods ◽  
Robin Boundary Condition ◽  
Robin Problem ◽  
Technical Approach ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Robin Boundary ◽  
Laplacian Equations

Abstract This paper is concerned with the existence and multiplicity of solutions for p(x)-Laplacian equations with Robin boundary condition. Our technical approach is based on variational methods.

SINGULAR LIMITS FOR 2-DIMENSIONAL ELLIPTIC PROBLEM WITH EXPONENTIALLY DOMINATED NONLINEARITY AND SINGULAR DATA

2011 ◽  
Vol 13 (04) ◽  
pp. 697-725 ◽  
Author(s):  
SAMI BARAKET ◽  
INES BEN OMRANE ◽  
TAIEB OUNI ◽  
NIHED TRABELSI
Keyword(s):  
Boundary Condition ◽  
Elliptic Problem ◽  
Source Term ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Singular Limits ◽  
Singular Source ◽  
Singular Data

We study existence of solutions with singular limits for a 2-dimensional semilinear elliptic problem with exponential dominated nonlinearity and a singular source term given by Dirac masses, imposing Dirichlet boundary condition. This paper extends previous results obtained in [3, 8]. We mainly use the method of domain decomposition.

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