Research on oscillation problems for degenerate hyperbolic equations

点击翻译按钮获取中文摘要

We have obtained sufficient conditions to be oscillating for the solutions of the boundary value problems for semilinear degenerate hyperbolic equations of second order. Especially, their problems under Dirichlet and Robin conditions were examined. We have also studied some existence condition of the positive solution to Tricomi type equation. Moreover, we have established the energy estimates of the solutions to degenerate wave equations with time dependent propagation speeds in ultradifferentiable classes, and found an optimal relation among the smoothness, degeneration and oscillation of their coefficients.