Anisotropic Robin problems with indefinite potential

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Abstract

We considered a nonlinear elliptic boundary value problem driven by the variable (anisotropic) (p,q)-Laplacian with Robin boundary condition and a superlinear reaction which does not satisfy the Ambrosetti-Rabinowitz condition. Using critical point theory, truncation and comparison techniques and critical groups, we showed the existence of five nontrivial smooth solutions all with sign information and ordered.

Keywords

variable exponents / regularity theory / constant sign and nodal solutions / critical point theory / critical groups

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