Nonlinear nonhomogeneous Robin problems with almost critical and partially concave reaction

Abstract

We consider a nonlinear Robin problem driven by a nonhomogeneous differential operator, with reaction which exhibits the competition of two Carathéodory terms. One is parametric, $(p-1)$-sublinear with a partially concave nonlinearity near zero. The other is $(p-1)$-superlinear and has almost critical growth. Exploiting the special geometry of the problem, we prove a bifurcation-type result, describing the changes in the set of positive solutions as the parameter $\lambda >0$ varies.

References in corpus (3)

• Positive solutions for nonlinear nonhomogeneous parametric Robin problems
• Multiple solutions for elliptic equations involving a general operator in divergence form
• Nonlinear nonhomogeneous boundary value problems with competition phenomena

Cited by in corpus (2)

• The behavior of solutions of a parametric weighted (p,q)-Laplacian equation
• Anisotropic $(p,q)$-equations with convex and negative concave terms