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

Volume 1, Issue 1, pp 36-44
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### 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.

### Share and Cite

##### ISRP Style

FANG ZHANG, MULTIPLE POSITIVE SOLUTIONS FOR NONLINEAR SINGULAR THIRD-ORDER BOUNDARY VALUE PROBLEM IN ABSTRACT SPACES, Journal of Nonlinear Sciences and Applications, 1 (2008), no. 1, 36-44

##### AMA Style

ZHANG FANG, MULTIPLE POSITIVE SOLUTIONS FOR NONLINEAR SINGULAR THIRD-ORDER BOUNDARY VALUE PROBLEM IN ABSTRACT SPACES. J. Nonlinear Sci. Appl. (2008); 1(1):36-44

##### Chicago/Turabian Style

ZHANG, FANG. "MULTIPLE POSITIVE SOLUTIONS FOR NONLINEAR SINGULAR THIRD-ORDER BOUNDARY VALUE PROBLEM IN ABSTRACT SPACES." Journal of Nonlinear Sciences and Applications, 1, no. 1 (2008): 36-44

### Keywords

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

•  34G20
•  34B16

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