in this work, by employing the krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prim...

A variational solution to the transient heat flow measure above a closed conductive region of arbitrary perimeter aspect, held at constant temperature, and which is embedded in an otherwise insulating boundary plane, presented. Upon developing general formulation, full range for circular disk conductor considered as example when implementing two term trial function that comprises form based on ...