# American Institute of Mathematical Sciences

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

 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.
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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