Existence results for Sturm–Liouville boundary value problem and rapid nonlinear oscillations

摘要

In this paper, we consider the existence of solutions to the following Sturm–Liouville boundary value problem of nonlinear systems x′=−h(y)+P(x,y,t), y′=g(x)−Q(x,y,t), x(0)sinα−y(0)cosα=0, x(1)sinβ−y(1)cosβ=0, 0⩽α<π, 0<β⩽π.