Divergent sequence of nontrivial solutions for superlinear double phase problems

Article type: Research Article

Authors: Papageorgiou, Nikolaos S.^a | Vetro, Calogero^{b; *} | Vetro, Francesca^c

Affiliations: [a] Department of Mathematics, National Technical University, Zografou campus, 15780, Athens, Greece | [b] Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy | [c] Independent Researcher, Palermo, 90100, Italy

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We consider a double phase (unbalanced growth) Dirichlet problem with a Carathéodory reaction f(z,x) which is superlinear in x but without satisfying the AR-condition. Using the symmetric mountain pass theorem, we produce a whole sequence of distinct bounded solutions which diverge to infinity.

Keywords: Double phase operator, generalized Orlicz spaces, Z₂-mountain pass theorem, C-condition, AR-condition

DOI: 10.3233/ASY-231830

Journal: Asymptotic Analysis, vol. 134, no. 1-2, pp. 183-192, 2023