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

Leszek Gasiński

doi:10.3934/dcds.2007.17.143

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

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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: March 2006

Revised: June 2006

Published: January 2007

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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.

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