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Positive solutions of singular complementary lidstone boundary value problems

Agarwal, RaviP
O'Regan, Donal
Staněk, Svatoslav
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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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Publisher
Springer Nature
Publisher DOI
10.1155/2010/368169
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Attribution-NonCommercial-NoDerivs 3.0 Ireland