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January  2007, 17(1): 143-158. doi: 10.3934/dcds.2007.17.143

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  October 2006

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: resonance, generalized nonsmooth Palais-Smale condition, first eigenvalue, positive solution, p-Laplacian, generalized nonsmooth mountain pass theorem..
Mathematics Subject Classification: Primary: 49J40; Secondary: 34B15, 34B18, 34A6.
Citation: Leszek Gasiński. Positive solutions for resonant boundary value problems with the scalar p-Laplacian and nonsmooth potential. Discrete & Continuous Dynamical Systems, 2007, 17 (1) : 143-158. doi: 10.3934/dcds.2007.17.143
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