Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

Minimax Theory and its Applications 01 (2016), No. 1, 083--109
Copyright Heldermann Verlag 2016

On Resonant (p,2)-Equations

Giuseppina Barletta
DICEAM, Facoltà di Ingegneria, Università di Reggio Calabria, Via Graziella - Loc. Feo di Vito, 89122 Reggio Calabria, Italy

Giuseppina D'Aguì
Dept. of Engineering and Applied Mathematics, University of Messina, 98166 Messina, Italy, Italy

Nikolaos S. Papageorgiou
Dept. of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece

We consider a nonlinear nonhomogeneous elliptic equation driven by the sum of a p-Laplacian and a Laplacian (p,2)-equation with a Carathéodory reaction which at ±∞ is resonant with respect to the principal eigenvalue of the negative Dirichlet p-Laplacian. Using minimax methods based on the critical point theory, together with truncation techniques and Morse theory, we obtain multiplicity results producing three or four solutions with sign information (constant sign solutions and nodal solutions).

Keywords: Minimax characterization, nonlinear regularity, nonlinear maximum principle, nodal solutions, resonant equation.

MSC: 35J20, 35J60; 58E05

[ Fulltext-pdf  (249  KB)] for subscribers only.