6533b7d8fe1ef96bd12698d8

RESEARCH PRODUCT

Solutions with sign information for nonlinear Robin problems with no growth restriction on reaction

Francesca VetroCalogero VetroNikolaos S. Papageorgiou

subject

nonlinear maximum principleApplied Mathematics010102 general mathematicsFunction (mathematics)Differential operator01 natural sciences010101 applied mathematicsNonlinear systemGrowth restrictionSettore MAT/05 - Analisi Matematicaextremal constant sign solutionsApplied mathematicsnodal solutions0101 mathematicscritical groupsAnalysisNonlinear regularity theorySign (mathematics)Parametric statisticsMathematics

description

We consider a parametric nonlinear Robin problem driven by a nonhomogeneous differential operator. The reaction is a Carathéodory function which is only locally defined (that is, the hypotheses concern only its behaviour near zero). The conditions on the reaction are minimal. Using variational tools together with truncation, perturbation and comparison techniques and critical groups, we show that for all small values of the parameter λ > 0, the problem has at least three nontrivial smooth solutions, two of constant sign and the third nodal.

https://doi.org/10.1080/00036811.2019.1597059