Anisotropic equations with indefinite potential and competing nonlinearities

Abstract

We consider a nonlinear Dirichlet problem driven by a variable exponent $p$-Laplacian plus an indefinite potential term. The reaction has the competing effects of a parametric concave (sublinear) term and of a convex (superlinear) perturbation (an anisotropic concave-convex problem). We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the positive parameter $\lambda$ varies. Also, we prove the existence of minimal positive solutions.

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Cited by in corpus (4)

• Anisotropic singular Neumann equations with unbalanced growth
• The behavior of solutions of a parametric weighted (p,q)-Laplacian equation
• Constant sign and nodal solutions for parametric anisotropic $(p,2)$-equations
• Anisotropic $(p,q)$-equations with convex and negative concave terms