Anisotropic $(p,q)$-equations with convex and negative concave terms

Abstract

We consider a parametric Dirichlet problem driven by the anisotropic $(p,q)$-Laplacian and with a reaction which exhibits the combined effects of a superlinear (convex) term and of a negative sublinear term. Using variational tools and critical groups we show that for all small values of the parameter, the problem has at least three nontrivial smooth solutions, two of which are of constant sign (positive and negative).

References in corpus (5)

• Anisotropic equations with indefinite potential and competing nonlinearities
• Asymmetric Robin problems with indefinite potential and concave terms
• Nonlinear nonhomogeneous Robin problems with almost critical and partially concave reaction
• Constant sign and nodal solutions for parametric anisotropic $(p,2)$-equations
• Superlinear perturbations of the eigenvalue problem for the Robin Laplacian plus an indefinite and unbounded potential