6533b822fe1ef96bd127ccb4
RESEARCH PRODUCT
Multiple nodal solutions for semilinear robin problems with indefinite linear part and concave terms
Francesca VetroCalogero VetroNikolaos S. Papageorgiousubject
Regularity theoryPure mathematicsApplied MathematicsConcave termPerturbation (astronomy)010103 numerical & computational mathematicsSign changingNodal solution01 natural sciencesOmega010101 applied mathematicsExtremal constant sign solutionSettore MAT/05 - Analisi MatematicaMountain pass theoremIndefinite potential0101 mathematicsNODALLaplace operatorAnalysisMathematicsdescription
We consider a semilinear Robin problem driven by Laplacian plus an indefinite and unbounded potential. The reaction function contains a concave term and a perturbation of arbitrary growth. Using a variant of the symmetric mountain pass theorem, we show the existence of smooth nodal solutions which converge to zero in $C^1(\overline{\Omega})$. If the coefficient of the concave term is sign changing, then again we produce a sequence of smooth solutions converging to zero in $C^1(\overline{\Omega})$, but we cannot claim that they are nodal.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-08-19 |