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 (4)

• Double phase transonic flow problems with variable growth: nonlinear patterns and stationary waves
• Double phase problems with variable growth
• Ground state and nodal solutions for a class of double phase problems
• A weighted anisotropic variant of the Caffarelli-Kohn-Nirenberg inequality and applications

Cited by in corpus (6)

• Parametric superlinear double phase problems with singular term and critical growth on the boundary
• Fractional double phase Robin problem involving variable order-exponents without Ambrosetti-Rabinowitz condition
• Robin double-phase problems with singular and superlinear terms
• Combined effects of singular and superlinear nonlinearities in singular double phase problems in ${\mathbb{R}}^N$
• Unbalanced fractional elliptic problems with exponential nonlinearity: subcritical and critical cases
• Morse homology: orientation of the moduli space of gradient flow lines, coherence and applications