Positive solutions of singular complementary lidstone boundary value problems
Agarwal, RaviP O'Regan, Donal Staněk, Svatoslav
Agarwal, RaviP
O'Regan, Donal
Staněk, Svatoslav
Publication Date
2010-01-01
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Article
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Agarwal, RaviP; O'Regan, Donal; Staněk, Svatoslav (2010). Positive solutions of singular complementary lidstone boundary value problems. Boundary Value Problems ,
Abstract
We investigate the existence of positive solutions of singular problem (-1)(m)x((2m+1)) = f(t, x, ..., x((2m))), x(0) = 0, x((2i-1))(0) = x((2i-1))(T) = 0, 1 <= i <= m. Here, m >= 1 and the Caratheodory function f(t, x(0), ..., x(2m)) may be singular in all its space variables x(0), ..., x(2m). The results are proved by regularization and sequential techniques. In limit processes, the Vitali convergence theorem is used.
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Springer Nature
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Attribution-NonCommercial-NoDerivs 3.0 Ireland