Oscillation And Nonoscillation Of The Fourth Order Nonlinear Differential Equation

This thesis is concerned with the oscillation and nonoscillation of the fourth order nonlinear differential equation where α>0, β＞0and p(t),q(t) are positive continuous functions defined on an infinite interval [α,∞), g(t) is a positive differential continuous function defined on an [α,∞) satisfying g’(t)>0, t≥a and limtâ†'∞g(t)=∞.The content is divided into four chapters. The first chapter introduces the research problems and background. The second chapter classifies the nonoscillatory solutions of the equation, gives their integral expressions, and establishes the existence criteria of nonoscillatory solutions with specific asymptotic properties. The third chapter gives sufficient conditions for oscillation of the equation. The fourth chapter is the conclusion of the thesis and sevaral problems to research are presented.