Opuscula Math. 40, no. 1 (2020), 131-149
https://doi.org/10.7494/OpMath.2020.40.1.131

Opuscula Mathematica

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

Florin-Iulian Onete
Nikolaos S. Papageorgiou
Calogero Vetro

Abstract. 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.

Keywords: superlinear reaction, constant sign and nodal solutions, extremal solutions, nonlinear regularity, nonlinear maximum principle, critical groups.

Mathematics Subject Classification: 35J20, 35J60.

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• Florin-Iulian Onete
• Liceul Tehnologic Petre Baniţǎ, 207170 Cǎlǎraşi, Dolj, Romania
• Nikolaos S. Papageorgiou
• National Technical University, Department of Mathematics, Zografou Campus, 15780, Athens, Greece
• Calogero Vetro (corresponding author)
• https://orcid.org/0000-0001-5836-6847
• University of Palermo, Department of Mathematics and Computer Science, Via Archirafi 34, 90123, Palermo, Italy
• Communicated by Marius Ghergu.
• Accepted: 2019-05-17.
• Published online: 2020-02-17.