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

E. N. Dancer; Zhitao Zhang

doi:10.3934/proc.2005.2005.209

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2005, Volume 2005: 209-215. Doi: 10.3934/proc.2005.2005.209 open access

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

E. N. Dancer^1, and
Zhitao Zhang^2,

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

Received: June 30, 2004

Revised: January 31, 2005

Published: August 2005

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Abstract

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 $-\Delta_p u=\lambda f(u), x\in \Om; u>0, x\in \Om; u=0, x\in \Po$.

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Mathematics Subject Classification: Primary: 35J65,35B32.

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