6533b850fe1ef96bd12a82a5

RESEARCH PRODUCT

Multiple solutions with sign information for a (p,2)-equation with combined nonlinearities

Francesca VetroNikolaos S. PapageorgiouCalogero Vetro

subject

Dirichlet problemNonlinear systemSublinear functionApplied MathematicsMathematical analysisRegular polygonPerturbation (astronomy)Laplace operatorAnalysisMathematicsParametric statistics

description

Abstract We consider a parametric nonlinear Dirichlet problem driven by the sum of a p -Laplacian and of a Laplacian (a ( p , 2 ) -equation) and with a reaction which has the competing effects of two distinct nonlinearities. A parametric term which is ( p − 1 ) -superlinear (convex term) and a perturbation which is ( p − 1 ) -sublinear (concave term). First we show that for all small values of the parameter the problem has at least five nontrivial smooth solutions, all with sign information. Then by strengthening the regularity of the two nonlinearities we produce two more nodal solutions, for a total of seven nontrivial smooth solutions all with sign informations. Our proofs use critical point theory, critical groups and flow invariance arguments.

yearjournalcountryeditionlanguage
2020-03-01Nonlinear Analysis
https://doi.org/10.1016/j.na.2019.111716