Constant Sign and Sign-Changing Solutions for Quasilinear Elliptic Equations with Neumann Boundary Condition

Giuseppina Barletta; Pasquale Candito; Dumitru Motreanu

Abstract

Through variational methods, sub-supersolution and truncation techniques we prove the existence of three nontrivial solutions for a quasilinear elliptic equation with Neumann boundary condition. We provide sign information for each of these solutions: two of them are of opposite constant sign and the third one is sign changing.

Author information

Contact details are reproduced from the original publication and may be historical.

Giuseppina Barletta

MECMAT, Università di Reggio Calabria, Via Graziella, Località Feo di Vito, 89100 Reggio Calabria, Italy

giuseppina.barletta@unirc.it

Pasquale Candito

MECMAT, Università di Reggio Calabria, Via Graziella, Località Feo di Vito, 89100 Reggio Calabria, Italy

pasquale.candito@unirc.it

Dumitru Motreanu

Dép. de Mathématiques, Université de Perpignan, Avenue Paul Alduy 52, 66860 Perpignan, France

motreanu@univ-perp.fr

Keywords

Quasilinear elliptic equations; sub-supersolution; critical point; Neumann problem; constant sign solutions; sign-changing solutions

Mathematics Subject Classification

35J62, 49J45

Suggested citation

G. Barletta, P. Candito, D. Motreanu. “Constant Sign and Sign-Changing Solutions for Quasilinear Elliptic Equations with Neumann Boundary Condition.” Journal of Convex Analysis 21 (2014), No. 1, 53–66.