Hostname: page-component-76fb5796d-22dnz Total loading time: 0 Render date: 2024-04-26T02:43:07.440Z Has data issue: false hasContentIssue false

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
Affiliation:
Department of Applied Mathematics, Hohai University, Nanjing, 210098, China, e-mail: Haishen2001@yahoo.com.cn
DONAL O'REGAN
Affiliation:
Department of Mathematics, National University of Ireland, Galway, Ireland e-mail: donal.regan@nunigalway.ie
RAVI P. AGARWAL
Affiliation:
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901-6975, USA e-mail: agarwal@fit.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Type
Research Article
Copyright
2005 Glasgow Mathematical Journal Trust

Footnotes

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