6533b85afe1ef96bd12b8c2d

RESEARCH PRODUCT

Constant sign and nodal solutions for nonlinear robin equations with locally defined source term

Francesca VetroCalogero VetroNikolaos S. Papageorgiou

subject

010102 general mathematicsMathematical analysisMathematics::Spectral Theory01 natural sciencesLocally defined reactionTerm (time)Critical groups010101 applied mathematicsNonlinear systemConstant sign and nodal solutionsSettore MAT/05 - Analisi MatematicaModeling and SimulationQA1-9390101 mathematicsNonlinear maximum principleConstant (mathematics)NODALMathematicsAnalysisSign (mathematics)MathematicsNonlinear regularity

description

We consider a parametric Robin problem driven by a nonlinear, nonhomogeneous differential operator which includes as special cases the p-Laplacian and the (p,q)-Laplacian. The source term is parametric and only locally defined (that is, in a neighborhood of zero). Using suitable cut-off techniques together with variational tools and comparison principles, we show that for all big values of the parameter, the problem has at least three nontrivial smooth solutions, all with sign information (positive, negative and nodal).

yearjournalcountryeditionlanguage
2020-05-13
10.3846/mma.2020.11031http://hdl.handle.net/10447/431815