Existence of multiple solutions for a class of second-order ordinary differential equations

Abstract

By means of variational structure and Z2 group index theory, we obtain multiple solutions for the second-order differential equation d/dt (p(t) du/dt) + q(t)u + ƒ(t, u) = 0, 0 < t < 1, subject to one of the following two sets of boundary conditions: u'(0) = u(1) + u'(1) = 0 or u(0) = u(1) = 0.