Positive solutions for nonlinear nonhomogeneous parametric Robin problems

Abstract

We study a parametric Robin problem driven by a nonlinear nonhomogeneous differential operator and with a superlinear Carathéodory reaction term. We prove a bifurcation-type theorem for small values of the parameter. Also, we show that as the parameter $\lambda >0$ approaches zero we can find positive solutions with arbitrarily big and arbitrarily small Sobolev norm. Finally we show that for every admissible parameter value there is a smallest positive solution $u_{\lambda }^{\ast }$ of the problem and we investigate the properties of the map $\lambda \mapsto u_{\lambda }^{\ast }$.

References in corpus (1)

• On a class of parametric $(p,2)$-equations

Cited by in corpus (2)

• Robin double-phase problems with singular and superlinear terms
• Nonlinear nonhomogeneous Robin problems with almost critical and partially concave reaction