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

Pages: 209 - 215, Issue Special, August 2005

 Abstract        Full Text (199.3K)              

E. N. Dancer - School of Mathematics and Statistics, University of Sydney, N.S.W. 2006, Australia (email)
Zhitao Zhang - Academy of Mathematics and Systems Science, Institute of Mathematics, the Chinese Academy of Sciences, Beijing 100080, China (email)

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

Keywords:  Quasilinear Elliptic Equation, Critical point, Anti-Maximum principle. Supported by Humboldt Foundation and National Natural Science Foundation of China.
Mathematics Subject Classification:  Primary: 35J65,35B32.

Received: July 2004;      Revised: February 2005;      Published: September 2005.