Existence and multiplicity of solutions for double-phase Robin problems

Abstract

We consider a double phase Robin problem with a Carathéodory nonlinearity. When the reaction is superlinear but without satisfying the Ambrosetti-Rabinowitz condition, we prove an existence theorem. When the reaction is resonant, we prove a multiplicity theorem. Our approach is Morse theoretic, using the notion of homological local linking.

References in corpus (2)

• Double phase transonic flow problems with variable growth: nonlinear patterns and stationary waves
• Ground state and nodal solutions for a class of double phase problems

Cited by in corpus (2)

• Robin double-phase problems with singular and superlinear terms
• Morse homology: orientation of the moduli space of gradient flow lines, coherence and applications