(p,2)-equations asymmetric at both zero and infinity

Author:

Papageorgiou Nikolaos S.1,Rădulescu Vicenţiu D.2,Repovš Dušan D.3

Affiliation:

1. Department of Mathematics, National Technical University, Zografou Campus, Athens15780, Greece

2. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, 014700Bucharest; and Department of Mathematics, University of Craiova, 200585 Craiova, Romania

3. Faculty of Education and Faculty of Mathematics and Physics, University of Ljubljana, SI-1000Ljubljana, Slovenia

Abstract

AbstractWe consider a {(p,2)}-equation, that is, a nonlinear nonhomogeneous elliptic equation driven by the sum of a p-Laplacian and a Laplacian with {p>2}. The reaction term is {(p-1)}-linear, but exhibits asymmetric behavior at {\pm\infty} and at {0^{\pm}}. Using variational tools, together with truncation and comparison techniques and Morse theory, we prove two multiplicity theorems, one of them providing sign information for all the solutions (positive, negative, nodal).

Funder

Javna Agencija za Raziskovalno Dejavnost RS

Consiliul National al Cercetarii Stiintifice

Publisher

Walter de Gruyter GmbH

Subject

Analysis

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