Positive Solutions of One‐Dimensional p‐Laplacian Boundary Value Problems for Fourth‐Order Differential Equations with Deviating Arguments

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.