Positive solutions of nonlocal singular boundary value problems
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2004-09-01Author
AGARWAL, RAVI P.
O'REGAN, DONAL
STANĚK, SVATOSLAV
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AGARWAL, RAVI P. O'REGAN, DONAL; STANĚK, SVATOSLAV (2004). Positive solutions of nonlocal singular boundary value problems. Glasgow Mathematical Journal 46 , 537-550
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.