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Some applications of dominated convergence theorems to a higher order singular boundary value problem

Yao Q.

Journal of Applied Analysis

2010

Vol. 16, nr 1

15-30

The existence of positive solution is considered for a singular higher-order boundary value problem, where the nonlinear term is a strong Carathéodory function. Two new existence theorems are proved by applying the Lebesgue dominated convergence theorem, the Fatou lemma and the Krasnosel'skii fixed point theorem of cone expansion or cone compression type.