A Novel Study on the Non-Negative Solution of an Eighth-Order BVP

Abstract

In this article, we investigate the existence of non-negative solutions for a boundary value problem associated with an eighth-order differential equation lambda((8))(omega) = psi(omega, lambda(omega), lambda((1))(omega), center dot center dot center dot , lambda((7))(omega)) for 0 < omega< 1, under initial values lambda(0) = lambda' (0) = lambda'' (0) = lambda''' (0) = 0 and lambda((4))(1) = lambda((5))(1) = lambda((6))(1) = lambda((7))(1) = 0, where psi is non-negative continuous function. For this study, we use the nonlinear Leray-Schauder alternative and the Leray-Schauder fixed-point theorem to prove the existence of at least one non-negative solution. As a numerical application, we present an example to confirm the utility of the achieved results.