# MULTIPLE POSITIVE SOLUTIONS FOR NONLINEAR SINGULAR THIRD-ORDER BOUNDARY VALUE PROBLEM IN ABSTRACT SPACES

Volume 1, Issue 1, pp 36-44 Publication Date: March 15, 2008

### Authors

FANG ZHANG - School of Mathematics and Physics, Jiangsu Polytechnic University, Changzhou, 213164, PR China.

### Abstract

In this paper, we study the nonlinear singular boundary value problem in abstract spaces: $\begin{cases} u''' + f(t, u) = \theta,\,\,\,\,\, t \in (0, 1),\\ u(0) = u'(0) = \theta, u'(1) = \xi u'(\eta), \end{cases}$ where $0 < \eta< 1$ and $1 < \xi<\frac{1}{\eta}, \theta$ denotes the zero element of $E, E$ is a real Banach space, and $f(t, u)$ is allowed to be singular at both end point $t = 0$ and $t = 1$. We show the existence of at least two positive solutions of this problem.

### Keywords

• Singular boundary value problem
• Abstract spaces
• Positive solutions
• Fixed point theorem.

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