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Positive solutions of singular three-point boundary value problems for second-order differential equations

โœ Scribed by Yan Sun; Lishan Liu; Jizhou Zhang; R.P. Agarwal

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
701 KB
Volume
230
Category
Article
ISSN
0377-0427

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โœฆ Synopsis

In this paper, we study the existence of positive solutions of a singular three-point boundary value problem for the following second-order differential equation

By constructing an available integral operator and combining fixed point index theory with properties of Green's function under some conditions concerning the first eigenvalues corresponding to the relevant linear operator, the sufficient conditions of the existence of positive solutions for the boundary value problems are established. The interesting point of the results is that the term a(t) may be singular at t = 0 and/or t = 1, moreover the nonlinear f (t, x) is also allowed to have singularity at x = 0.

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