Oscillation for systems of nonlinear neutral type parabolic partial functional differential equations

This paper discusses the oscillation of solutions for systems of nonlinear neutral type parabolic partial fuctional differential equations of the form     

Oscillation properties of solutions of a class of nonlinear parabolic equations

Oscillations of solutions of a class of nonlinear parabolic equations are investigated, and the unboundedness of solutions is also studied as corollaries. Our approach is to employ the modifications of Picone-type identities for half-linear elliptic operators.     

On a system of quasilinear parabolic functional differential equations

Summary We consider initial boundary value problems for a system of second order quasilinear parabolic equations where also the main part contains functional dependence on the unknown function. This system is of type, considered in [6], [7] by U. Hornung, W. J?ger and A. Mikelic.     

Oscillation of certain fourth-order functional differential equations

Some new criteria for the oscillation of fourth-order nonlinear functional differential equations of the form

Oscillation of solutions of parabolic differential equations of neutral type

In this paper, we investigate a class of parabolic differential equations of neutral type, and obtain some sufficient conditions of the oscillation for such equations satisfying two kinds of boundary value conditions.     

On a class of functional and differential functional equations

One class of functional and differential functional equations with deviating argument depending on the unknown function is considered in this study. The procedure of constructing and investigating solutions to such equations is also proposed.     

Oscillation criteria for fourth-order functional differential equations

Some new criteria for the oscillation of all solutions of certain fourth-order functional differential equations are established.     

Oscillation theorems for second-order functional differential equations

This paper presents some comparison theorems on the oscillatory behavior of solutions of second-order functional differential equations. Here we state one of the main results in a simplified form: Let q, τ₁, τ₂ be nonnegative continuous functions on (0, ∞) such that τ₁ ? τ₂ is a bounded function on [1, ∞) and t ? τ₁(t) → ∞ if t → ∞. Then $\text{y}\text{?}\text{(t) + q(t) y(t ? τ}{}_1\text{(t)) = 0}$ is oscillatory if and only if $\text{y}\text{?}\text{(t) + q(t) y(t ? τ}{}_2\text{(t)) = 0}$ is oscillatory.     

Oscillation criteria of a class of fourth order differential equations

In the present paper, we consider the oscillation of a class of self‐adjoint fourth order differential equation. Some oscillation and non‐oscillation criteria on a perturbation equation of Euler differential equation are given. In particular, we find the exact value of a constant in some oscillation criteria, which has answered the open problem presented by Do?lý in 2004. Copyright © 2011 John Wiley & Sons, Ltd.     

Oscillation of solutions of neutral parabolic differential equations with oscillating coefficients

Sufficient conditions are obtained for oscillation of solutions of a class of neutral parabolic differential equations with oscillating coefficients.      

Oscillation criteria for a class of nonlinear system of differential equations

Using the integral average method, we establish some oscillation criteria of Kamenev type and Yan type for the nonlinear system of differential equation

where the functions b_i(t) (i = 1, 2) are nonnegative and summable on each finite segment of the interval Z0, ∞), λ_i > 0 (i = 1,2) with λ₁ λ₂ = 1.     

Oscillation theorems for fourth order functional differential equations

The authors investigate the oscillatory behavior of all solutions of the fourth order functional differential equations $\frac{d^{3}}{dt^{3}}(a(t)(\frac{dx(t)}{dt})^{\alpha})+q(t)f(x[g(t)])=0$ and $\frac{d^{3}}{dt^{3}}(a(t)(\frac{dx(t)}{dt})^{\alpha})=q(t)f(x[g(t)])+p(t)h(x[\sigma(t)])$ in the case where ∫ ^∞ a ^?1/α (s)ds<∞. The results are illustrated with examples.