Existence theorems for a class of nonlocal differential equations

Abstract

A class of nonlocal second-order ordinary differential equations of the formfor continuous f and λ is studied. The equation is supplemented with none, one, or two Robin boundary conditions depending on whether the interval of interest I is finite, semi-infinite or infinite. The only other restriction on the function λ is that it maps I into itself. Sufficient conditions for the existence of a solution are found, which include the assumption of the existence of 'upper' and 'lower' solutions. The upper and lower solutions provide bounds for the solution on I .

Eigenfunctions Arising From a First-Order Functional Differential Equation in a Cell Growth Model

“…Da Costa et al [11] showed that the solution must be unimodal. Properties of solutions have also been studied by Chang and Jau [10] and Begg [5]. The model has been applied to tumour growth [3] and the growth of plankton [4].…”