TY  - JOUR
ID  - Onete2020
LB  - Onete2020
AU  - Onete, Florin-Iulian
AU  - Papageorgiou, Nikolaos S.
AU  - Vetro, Calogero
TI  - A multiplicity theorem for parametric superlinear (p,q)-equations
ST  - A multiplicity theorem for parametric superlinear (p,q)-equations
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2020
VL  - 40
IS  - 1
SP  - 131
EP  - 149
DO  - https://doi.org/10.7494/OpMath.2020.40.1.131
UR  - https://doi.org/10.7494/OpMath.2020.40.1.131
AB  - 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.
KW  - superlinear reaction
KW  - constant sign and nodal solutions
KW  - extremal solutions
KW  - nonlinear regularity
KW  - nonlinear maximum principle
KW  - critical groups
SN  - 1232-9274
ER  -