Existence and nonexistence of positive solutions for parametric Neumann problems with $p$-Laplacian

Dumitru Motreanu (1) , Viorica V. Motreanu (2) , Nikolaos S. Papageorgiou (3)

1 LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations
2 Department of Mathematics [Be'er Sheva]
3 Department of Mathematics

Using variational methods based on the critical point theory and suitable truncation and comparison techniques, we study existence, multiplicity and nonexistence of positive solutions for a parametric nonlinear Neumann problem driven by the $p$-Laplacian. Our hypotheses cover the case of nonlinearities of concave-convex type whose exponents depend on the parameter.

Keywords: p-Laplacian; concave-convex nonlinearities; positive solutions; bifurcation-type theorem

Domains: Mathematics [math]

Dumitru Motreanu, Viorica V. Motreanu, Nikolaos S. Papageorgiou. Existence and nonexistence of positive solutions for parametric Neumann problems with $p$-Laplacian. Tohoku mathematical journal, 2014, 66 (1), pp.137-153. ⟨10.2748/tmj/1396875667⟩. ⟨hal-01142925⟩