scholarly journals Multiple solutions for a class of semilinear elliptic problems with Robin boundary condition

2012 ◽  
Vol 388 (1) ◽  
pp. 435-442 ◽  
Author(s):  
Jing Zhang ◽  
Shujie Li ◽  
Xiaoping Xue
Keyword(s):  
Boundary Condition ◽  
Multiple Solutions ◽  
Elliptic Problems ◽  
Robin Boundary Condition ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic Problems ◽  
Robin Boundary

scholarly journals Multiple solutions to a quasilinear Schrödinger equation with Robin boundary condition

2020 ◽  
Vol 5 (4) ◽  
pp. 3825-3839
Author(s):  
Yin Deng ◽  
◽  
Gao Jia ◽  
Fanglan Li ◽  
◽  
...  
Keyword(s):  
Boundary Condition ◽  
Multiple Solutions ◽  
Robin Boundary Condition ◽  
Dinger Equation ◽  
Robin Boundary

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.

Multiple solutions for an elliptic system with indefinite Robin boundary conditions

2017 ◽  
Vol 8 (1) ◽  
pp. 603-614 ◽  
Author(s):  
Pablo Amster
Keyword(s):  
Boundary Condition ◽  
Elliptic System ◽  
Multiple Solutions ◽  
Robin Boundary Condition ◽  
Robin Boundary Conditions ◽  
Precise Calculation ◽  
Scalar Operator ◽  
Point Operator ◽  
Robin Boundary ◽  
Linear Scalar

Abstract Multiplicity of solutions is proved for an elliptic system with an indefinite Robin boundary condition under an assumption that links the linearisation at 0 and the eigenvalues of the associated linear scalar operator. Our result is based on a precise calculation of the topological degree of a suitable fixed point operator over large and small balls.

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