Oscillation criteria for second order nonlinear differential equations

Summary Various sufficient conditions are obtained which guarantee that all continuable solutions of (1.1) y″+q(t)y′+p(t)f(y)=0 are oscillatory. No explicit sign assumptions are made on p(t) although certain integral conditions are assumed to hold with regard to f(y), p(t) and q(t). Examples are given of the form p(t) = λ/t^μ + (βsint)/t^α, λ, β, μ, α>0. This research was supported by NRC Grant A-7673 and CMC Summer Research Grant. Entrata in Redazione il 4 settembre 1971.     

Oscillation theorems for second order nonlinear differential equations

Some oscillation criteria are established for certain second order nonlinear differential equations of the form (a(t)ψ(x(t)) x^. (t))^. + p(t) x^. (t) + q(t)f(x(t)) = 0. These criteria improve upon some of the known results by Kura, Kamenev and Philos.     

Oscillation criteria for nonlinear second order damped differential equations

For all solutions of a class of second order nonlinear damped differential equations, new oscillation criteria are established. Asymptotic behavior for forced equations is also discussed.     

Oscillation criteria for second order nonlinear neutral differential equations

By refining the standard integral averaging technique, we obtain new oscillation criteria for a class of second order nonlinear neutral differential equations of the form

(r(t)(x(t)+p(t)x(t-τ))^′)^′+q(t)f(x(t),x(σ(t)))=0.     

Oscillation of nonlinear second order matrix differential equations

In this paper, sufficient conditions are obtained for oscillation of all nontrivial, prepared, symmetric solutions of a class of nonlinear second order matrix differential equations of the form

Oscillation criteria for nonlinear second order differential equations with damping

Summary Using the integral average method, we give some new oscillation criteria for the second order differential equation with damped term (a(t)Ψ(x(t))K(x'(t)))'+p(t)K(x'(t))+q(t)f(x(t))=0, t<span style='font-size:10.0pt; font-family:"Lucida Sans Unicode"'>≧t₀. These results improve and generalize the oscillation criteria in<span lang=EN-US style='font-size:10.0pt;mso-ansi-language:EN-US'>[1], because they eliminate both the differentiability of p(t) and the sign of p(t), q(t). As a consequence, improvements of Sobol's type oscillation criteria are obtained.     

中立型二阶非线性微分方程振动性的判据

Abstract. In this paper ,the oscillation criteria for the solutions of the nonlinear differential e-quations of neutral type of the forms:     

Oscillation criteria for nonlinear second order equations

Summary A necessary and a sufficient condition are given for oscillation of all solutions of y″+f(t, y)=0. We sequire that a(t)α(y)≤f(t, y) if y>0, and f(t, y)<-b(t)β(y) if y<0, together with continuity and integrability assumptions on a, b, α, and β. Of speciat interest here is the relaxing of conditions a≥0, b≥0 in Machi - Wong [6]. Entrata in Redazione il 9 ottobre 1968. Supported by NASA Research Grant NGR-45-003-038.     

Oscillations of certain second order nonlinear differential equations

A second order nonlinear differential equation

Solitary wave and other solutions for nonlinear heat equations

A number of explicit solutions for the heat equation with a polynomial non-linearity and for the Fisher equation is presented. An extended class of non-linear heat equations admitting solitary wave solutions is described. The generalization of the Fisher equation is proposed whose solutions propagate with arbitrary ad hoc fixed velocity.     

二阶非线性椭圆型微分方程解的振动比较定理

建立几个微分不等式,讨论了一类二阶非线性椭圆型微分方程解的振动性,得到几个新的振动比较定理．     

二阶非线性泛函微分方程解的振动性质

研究了一类二阶非线性泛函微分方程解的振动性以及非振动解的有界性.在一定条件下,建立了几个新的振动性和有界性定理,其结果推广和改进了已有的一些结果.     

Oscillation criteria for differential equations of second order

In this article, we give sufficient condition in the form of integral inequalities to establish the oscillatory nature of non linear homogeneous differential equations of the form

Oscillation theorems for second order nonlinear dynamic equations

Some new criteria for the oscillation of nonlinear dynamic equations of the form $$\bigl(a(t)(x^{\Delta}(t))^{\alpha}\bigr)^{\Delta}+f(t,x^{\sigma}(t))=0$$ on a time scale $\mathbb{T}$ are established.     

Oscillation of second-order nonlinear neutral differential equations

In this paper, some sufficient conditions for oscillation and nonoscillation are obtained for the second-order nonlinear neutral differential equation

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