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Jankowski, T.

Positive solutions of one-dimensional \(p\)-Laplacian boundary value problems for fourth-order differential equations with deviating arguments. (English) Zbl 1221.34063

J. Optim. Theory Appl. 149, No. 1, 47-60 (2011).
Summary: This paper considers the existence of positive solutions of four-point boundary value problems for fourth-order ordinary differential equations with deviating arguments and \(p\)-Laplacian. We discuss such problems in the cases when the deviating arguments are delayed or advanced, what may concern optimization issues related to some technical problems. To obtain the existence results, a fixed-point theorem for cones due to Avery and Peterson is applied. According to the author’s knowledge, the results are new. It is a first paper where a fixed-point theorem for cones is applied to fourth-order differential equations with deviating arguments and \(p\)-Laplacian. An example is included to verify the theoretical results.

Cited in 4 Documents

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34K10 Boundary value problems for functional-differential equations

Keywords:

fourth-order differential equations; delayed arguments; advanced arguments; positive solutions
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References:

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