Abstract
In this paper we deal with Robin and Neumann parametric elliptic equations driven by a nonhomogeneous differential operator and with a reaction that exhibits competing nonlinearities (concave-convex nonlinearities). For the Robin problem and without employing the Ambrosetti-Rabinowitz condition, we prove a bifurcation theorem for the positive solutions for small values of the parameter $\lambda>0$. For the Neumann problem with a different geometry and using the Ambrosetti-Rabinowitz condition we prove bifurcation for large values of $\lambda>0$.
Highlights
Let Ω ⊆ RN be a bounded domain with C2-boundary ∂Ω
We study the following nonlinear, nonhomogeneous parametric Robin problem:
We prove two bifurcation type results, describing the set of positive solutions of (Pλ) as the parameter λ > 0 changes, when the reaction exhibits the competing effects of concave and convex nonlinearities
Summary
National Technical University, Department of Mathematics Zografou Campus, Athens 15780, Greece
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