A multiplicity theorem for parametric superlinear (p,q)-equations

Opuscula Mathematica

article

Florin-Iulian Onete¹  Nikolaos S. Papageorgiou²  Calogero Vetro (corresponding author)³ 

[1] Liceul Tehnologic Petre Baniţǎ;National Technical University, Department of Mathematics, Zografou Campus;University of Palermo, Department of Mathematics and Computer Science

关键词: superlinear reaction;    constant sign and nodal solutions;    extremal solutions;    nonlinear regularity;    nonlinear maximum principle;    critical groups.;   

DOI  :  10.7494/OpMath.2020.40.1.131

学科分类：环境科学（综合）

来源: AGH University of Science and Technology Press

【 摘 要 】

We consider a parametric nonlinear Robin problem driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (\((p,q)\)-equation). The reaction term is \((p-1)\)-superlinear but need not satisfy the Ambrosetti-Rabinowitz condition. Using variational tools, together with truncation and comparison techniques and critical groups, we show that for all small values of the parameter, the problem has at least five nontrivial smooth solutions, all with sign information.

【 授权许可】

CC BY-NC