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

1School of Mathematics and Physics, Changzhou University, Changzhou, 213164, P.R. China

2Department of Applied Mathematics, Shandong University of Science and Technology, Qingdao, 266510, P.R. China

© 2010 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

Citation Information: Mathematica Slovaca. Volume 60, Issue 4, Pages 485–494, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.2478/s12175-010-0027-5, July 2010

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Published Online:


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.

MSC: Primary 34B10, 34B18

Keywords: singular; nontrivial solutions; positive solutions; topology degree

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