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The boundary value problem of higher order differential equations with delay

He Z., Shen J.

Demonstratio Mathematica

2013

Vol. 46, nr 1

87--100

In the paper, Guo–Krasnoselskii’s fixed point theorem is adapted to study the existence of positive solutions to a class of boundary value problems for higher order differential equations with delay. The sufficient conditions, which assure that the equation has one positive solution or two positive solutions, are derived. These conclusions generalize some existing ones.

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.