Qualitative Analysis On Several Kinds Of The Second Order Nonlinear Differential Equations

This thesis of Master is composed of four chapters,which mainly studies several kinds of the second order nonlinear differential equations about the oscillatory and asymptotic behavior of solutions,the existence of limit cycles and the period function of a center.A series of new results are obtained, and some of them improve or extend the related results in the literatures.Chapter 1 introduces the background of the problem-researching and the recent development of the research in this field.Chapter 2 considers oscillatory and asymptotic behavior of solutions of the equation(a(t)(x′(t))^σ)′ +p(x(t))x′(t) + q(t)f(x(t)) = 0where σ are respectively positive quotients of even over odd integers and odd over odd integers, some sufficient conditions are established.Chapter 3 concerns the nonexistence of limit cycle of the Lienard equation x″ + f₁(x)x′2+εf₂(x)x′ + g(x) = 0the period function of a center is also studied.Chapter 4 considers the existence of limit cycles of the Lienard equationx″ + f₁(x)(x′)^σ+f₂(x)x′ + g(x) = 0where σ is a positive quotient of odd over odd integers.