Vol. 264, No. 2, 2013

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On nonlinear nonhomogeneous resonant Dirichlet equations

Nikolaos S. Papageorgiou and George Smyrlis

Vol. 264 (2013), No. 2, 421–453
Abstract

We consider a (p,2)-equation with a Carathéodory reaction f(z,x) which is resonant at ±∞ and has constant sign, z-dependent zeros. Using variational methods, together with truncation and comparison techniques and Morse theory, we establish the existence of five nontrivial smooth solutions (four of constant sign and the fifth nodal). If the reaction f(z,x) is C1 in x , then we produce a second nodal solution for a total of six nontrivial smooth solutions.

Keywords
resonant equations, tangency principle, strong comparison principle, constant sign and nodal solutions, Morse theory
Mathematical Subject Classification 2010
Primary: 35J20, 35J60, 35J92, 58E05
Milestones
Received: 27 April 2012
Revised: 7 January 2013
Accepted: 7 February 2013
Published: 28 July 2013
Authors
Nikolaos S. Papageorgiou
Department of Mathematics
National Technical University of Athens
Zografou Campus
15780 Athens
Greece
George Smyrlis
Department of Mathematics
National Technical University of Athens
Zografou Campus
15780 Athens
Greece