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Positive solutions of nonlocal singular boundary value problems

By RAVI P. AGARWAL, DONAL O'REGAN and SVATOSLAV STANĚK

Abstract

The paper presents the existence result for positive solutions of the differential equation (g(x))" = f(t, x, (g(x))') satisfying the nonlocal boundary conditions x(0) = x(T), min{x(t) : t E J} = 0. Here the positive function f satisfies local Caratheodory conditions on [0, T] x (0, infinity) x (R\{0}) and f may be singular at the value 0 of both its phase variables. Existence results are proved by Leray-Schauder degree theory and Vitali's convergence theorem

Topics: existence theory, equations, dirichlet
Publisher: 'Cambridge University Press (CUP)'
Year: 2004
DOI identifier: 10.1017/s0017089504001983
OAI identifier: oai:aran.library.nuigalway.ie/:10379/8805
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