Positive solutions for resonant boundary value problems with the scalar p-Laplacian and nonsmooth potential

Leszek Gasiński

doi:10.3934/dcds.2007.17.143

Article Contents

2007, Volume 17, Issue 1: 143-158. Doi: 10.3934/dcds.2007.17.143

This issue Previous Article The connected Isentropes conjecture in a space of quartic polynomials Next Article The global attractor for the solutions to the 3D viscous primitive equations

Positive solutions for resonant boundary value problems with the scalar p-Laplacian and nonsmooth potential

Leszek Gasiński^1,

1.
Jagiellonian University, Institute of Computer Science, ul. Nawojki 11, 30072 Kraków

Received: February 28, 2006

Revised: May 31, 2006

Published: December 2006

Abstract Related Papers Cited by

Abstract

In this paper we study boundary value problem with one dimensional $p$-Laplacian. Assuming complete resonance at $+\infty$ and partial resonance at $0^+$, an existence of at least one positive solution is proved. By strengthening our assumptions we can guarantee strict positivity of the obtained solution.

Keywords:

p-Laplacian,
positive solution,
resonance,
first eigenvalue,
generalized nonsmooth Palais-Smale condition,
generalized nonsmooth mountain pass theorem.

Mathematics Subject Classification: Primary: 49J40; Secondary: 34B15, 34B18, 34A60.

Citation:

Article Metrics

HTML views() PDF downloads(71) Cited by(0)

Positive solutions for resonant boundary value problems with the scalar p-Laplacian and nonsmooth potential

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Positive solutions for resonant boundary value problems with the scalar p-Laplacian and nonsmooth potential

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content