Ground state and nodal solutions for a class of double phase problems

Abstract

We consider a double phase problem driven by the sum of the $p$-Laplace operator and a weighted $q$-Laplacian ($q<p$), with a weight function which is not bounded away from zero. The reaction term is $(p-1)$-superlinear. Employing the Nehari method, we show that the equation has a ground state solution of constant sign and a nodal (sign-changing) solution.

Cited by in corpus (2)

• Existence and multiplicity of solutions for double-phase Robin problems
• Anisotropic singular Neumann equations with unbalanced growth