On the existence of solutions for singular boundary value problem of third-order differential equations : Mathematica Slovaca

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# Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

IMPACT FACTOR 2014: 0.409

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# On the existence of solutions for singular boundary value problem of third-order differential equations

1Changzhou University

2Shandong University of Science and Technology

Citation Information: Mathematica Slovaca. Volume 60, Issue 4, Pages 485–494, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, July 2010

### Publication History

Published Online:
2010-07-08

## Abstract

The singular boundary value problems of third-order differential equations $$\begin{array}{*{20}c} { - u'''(t) = h(t)f(t,u(t)), t \in (0,1),} \\ {u(0) = u'(0) = 0, u'(1) = \alpha u'(\eta )} \\ \end{array}$$ are considered under some conditions concerning the first eigenvalues corresponding to the relevant linear operators, where h(t) is allowed to be singular at both t = 0 and t = 1, and f is not necessary to be nonnegative. The existence results of nontrivial solutions and positive solutions are given by means of the topological degree theory.

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