On the solvability of a parameter-dependent cantilever-type BVP

TL;DR

This paper investigates the conditions under which a parameter-dependent cantilever boundary value problem has solutions, providing existence, localization, and bounds for parameters, supported by an illustrative example.

Contribution

It introduces new existence and localization results for positive solutions of the BVP using a Birkhoff-Kellogg type theorem and establishes bounds under growth conditions.

Findings

Existence of positive solutions is guaranteed under certain conditions.

Localization results specify where solutions can be found.

Parameter bounds are derived under growth restrictions.

Abstract

We discuss the solvability of a parameter dependent cantilever-type boundary value problem. We provide an existence and localization result for the positive solutions via a Birkhoff-Kellogg type theorem. We also obtain, under additional growth conditions, upper and lower bounds for the involved parameters. An example is presented in order to illustrate the theoretical results.