Lower and upper functions in a singular Dirichlet problem with o-Laplacian

Abstract

The paper investigates the Dirichlet problem with ø-Laplacian of the form $(\varphi (u'))' + f(t,u,u') = 0,u(0) = u(T) = 0.$ An existence principle which can be used for problems where f(t, x, y) may have singularities at t = 0, t = T and also at x = 0, y = 0, is proved here. As an application of this principle, new conditions that guarantee the solvability of the above problem are found.