Anisotropic Dirichlet double phase problems with competing nonlinearities

We consider a Dirichlet double phase problem with variable exponents and nonstandard growth. The reaction has the competing effects of a parametric concave term and a superlinear perturbation (concave-convex problem). We show that for all small values of the parameter the problem has at least two nontrivial bounded solutions.

Automated summary

This article considers a Dirichlet double phase problem with variable exponents and nonstandard growth. The reaction has the competing effects of a parametric concave term and a superlinear perturbation, resulting in a concave-convex problem. It is shown that for all small values of the parameter, the problem has at least two nontrivial bounded solutions.