Title

Elliptic equations with indefinite and unbounded potential and a nonlinear concave boundary condition

Abstract

We consider an elliptic problem driven by the negative Laplacian plus an indefinite and unbounded potential and a superlinear reaction. The boundary condition is parametric, nonlinear and superlinear near zero. Thus, the problem is a new version of the classical "convex-concave" problem (problem with competing nonlinearities). First, we prove a bifurcation-type result describing the set of positive solutions as the parameter λ>0 varies. We also show the existence of a smallest positive solution ūλ and investigate the properties of the map λ→ūλ. Finally, by imposing bilateral conditions on the reaction we generate two more solutions, one of which is nodal.

Document Type

Article

DOI

10.1142/s021919971550090x

Keywords

nonlinear boundary condition, competing nonlinearity, bifurcation-type theorem, extremal constant sign solutions, nodal solutions, indefinite and unbounded potential

Publication Date

2017

Recommended Citation

Hu, Shouchuan, and Nikolaos S. Papageorgiou. "Elliptic equations with indefinite and unbounded potential and a nonlinear concave boundary condition." Communications in Contemporary Mathematics 19, no. 01 (2017): 1550090.

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