# American Institute of Mathematical Sciences

2005, 2005(Special): 209-215. doi: 10.3934/proc.2005.2005.209

## Critical point, anti-maximum principle and semipositone p-laplacian problems

 1 School of Mathematics and Statistics, University of Sydney, N.S.W. 2006, Australia 2 Academy of Mathematics and Systems Science, Institute of Mathematics, the Chinese Academy of Sciences, Beijing 100080, China

Received  July 2004 Revised  February 2005 Published  September 2005

In this paper, we use Nehari manifold to extend the anti-maximum principle of Laplacian operator to an existence theorem for p-Laplacian ($p\not=2$), then consider the existence of nonnegative solutions to semipositone quasilinear elliptic problems $-\Delta_p u=\lambda f(u), x\in \Om; u>0, x\in \Om; u=0, x\in \Po$.
Citation: E. N. Dancer, Zhitao Zhang. Critical point, anti-maximum principle and semipositone p-laplacian problems. Conference Publications, 2005, 2005 (Special) : 209-215. doi: 10.3934/proc.2005.2005.209
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