MULTIPLE POSITIVE SOLUTIONS FOR NONLINEAR SINGULAR THIRD-ORDER BOUNDARY VALUE PROBLEM IN ABSTRACT SPACES
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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.
MSC
References
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