scholarly journals The Nehari manifold for a semilinear elliptic problem with the nonlinear boundary condition

2013 ◽  
Vol 400 (1) ◽  
pp. 100-119 ◽  
Author(s):  
Jinguo Zhang ◽  
Xiaochun Liu
Keyword(s):  
Boundary Condition ◽  
Elliptic Problem ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Nehari Manifold ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
The Nehari Manifold

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 Existence of Multiple Solutions for a -Kirchhoff Problem with Nonlinear Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Zonghu Xiu ◽  
Caisheng Chen
Keyword(s):  
Variational Method ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Multiple Solutions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Nehari Manifold ◽  
The Nehari Manifold ◽  
Kirchhoff Problem

The paper considers the existence of multiple solutions of the singular nonlocal elliptic problem , ,   = , on , where , . By the variational method on the Nehari manifold, we prove that the problem has at least two positive solutions when some conditions are satisfied.

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.

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