Nonlinear  Neumann problems with indefinite potential and concave terms

Shouchuan Hu; Nikolaos S. Papageorgiou

doi:10.3934/cpaa.2015.14.2561

Article Contents

2015, Volume 14, Issue 6: 2561-2616. Doi: 10.3934/cpaa.2015.14.2561

This issue Previous Article Dynamics of a host-pathogen system on a bounded spatial domain Next Article

Nonlinear Neumann problems with indefinite potential and concave terms

Shouchuan Hu^1, and
Nikolaos S. Papageorgiou^2,

1.
College of Mathematics, Shandong Normal University, Jinan, Shandong
2.
Department of Mathematics, National Technical University of Athens, Zografou Campus, Athens 15780

Received: December 2014

Revised: July 2015

Published: November 2015

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Abstract

In this paper we conduct a detailed study of Neumann problems driven by a nonhomogeneous differential operator plus an indefinite potential and with concave contribution in the reaction. We deal with both superlinear and sublinear (possibly resonant) problems and we produce constant sign and nodal solutions. We also examine semilinear equations resonant at higher parts of the spectrum and equations with a negative concavity.

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Mathematics Subject Classification: 35J20, 35J60, 58E05.

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