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UPPER AND LOWER SOLUTIONS FOR THE SINGULAR p-LAPLACIAN WITH SIGN CHANGING NONLINEARITIES VIA INEQUALITY THEORY

Published online by Cambridge University Press:  29 November 2005

HAISHEN LÜ ,
DONAL O'REGAN  and
RAVI P. AGARWAL
HAISHEN LÜ
Affiliation:
Department of Applied Mathematics, Hohai University, Nanjing, 210098, China, e-mail: [email protected]
DONAL O'REGAN
Affiliation:
Department of Mathematics, National University of Ireland, Galway, Ireland e-mail: [email protected]
RAVI P. AGARWAL
Affiliation:
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901-6975, USA e-mail: [email protected]
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Abstract

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In this paper, general existence theorems are presented for the singular equation \[\left\{\begin{array}{@{}l}-(\varphi_p(u^{\prime}))^{\prime}=f(t,u,u^{\prime}),\;0<t<1\\[3pt]u(0)=u(1)=0.\end{array}\right.\] Throughout, our nonlinearity is allowed to change sign. The singularity may occur at $u=0,$$t=0$ and $t=1$.

Keywords

34B1534B16
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 47 , Issue 3 , September 2005 , pp. 439 - 460
Copyright
2005 Glasgow Mathematical Journal Trust

Footnotes

The research is supported by NNSF of China (10301033).