Oscillation criteria of second order nonlinear neutral differential equations with damping terms(具阻尼项的二阶非线性中立型微分方程的振动准则)

Abstract

The purpose of this paper is to establish some new oscillation criteria for the second-order nonlinear neutral differential equations with damping terms which have the form [a(t)z'(t)α-1z'(t)]'+b(t)z'(t)α-1z'(t)+q(t)x(σ(t))β-1x(σ(t))=0， where z(t)=x(t)+p(t)x(τ(t)). Our theorems improve, extent and unify a number of related results reported in the literature. The wide application of the obtained criteria is illustrated via examples.(建立了二阶非线性中立型阻尼微分方程[a(t)z'(t)α-1z'(t)]'+b(t)z'(t)α-1z'(t)+q(t)x(σ(t))β-1x(σ(t))=0的若干振动准则，其中z(t)=x(t)+p(t)x(τ(t))。改进、推广和统一了已有文献的相关结果，并通过实例说明了所得准则的广泛应用效果。)

Keywords

• oscillation criterion(振动准则)
• damped equation(阻尼方程)
• neutral differential equation(中立型微分方程)
• emden-fowler equation(emden-fowler方程)
• half-linear differential equation(半线性微分方程)