I. Kubiaczyk

New oscillation criteria for first order nonlinear neutral delay differential equations

Some new oscillation criteria of first order nonlinear neutral delay differential equations with variable coefficients are given. Our results extend and improve some of the well known previously results in the literature. Some examples are considered to illustrate our main results.

Oscillation of delay parabolic differential equations with several coefficients

Some new sufficient conditions are established for the oscillation of delay parabolic differential equations of the form ∂u(x,t)/∂t= a(t) Δu - Σi=1n pi(x,t)u(x,t - σi) + Σj=1m qj)(x,t)u(x,t - τj), (x,t) ∈ Ω × [t0,∞)≡ G where Ω is a bounded domain in Rn with a piecewise smooth boundary ∂Ω, and Δ is the Laplacian in Euclidean n-space Rn with three different boundary conditions. Our results improve the well-known oscillation result of (E) when n = m = 1. An example is considered to illustrate our main results.

OSCILLATION OF SOLUTIONS TO NONLINEAR NEUTRAL DELAY DIFFERENTIAL EQUATIONS

Abstract In this paper we shall consider the nonlinear neutral delay differential equations with variable coefficients. Some new sufficient conditions for oscillation of all solutions are obtained. Our results extend and improve some of the well known results in the literature. Some examples are considered to illustrate our main results. The neutral logistic equation with variable coefficients is considered to give some new sufficient conditions for oscillation of all positive solutions about its positive steady state.

Oscillation criteria for nonlinear neutral functional dynamic equations on time scales

In this paper, we establish some new sufficient conditions for oscillation of the second-order neutral functional dynamic equation

Oscillation and stability in nonlinear delay differential equations of population dynamics

\left[ {r\left( t \right)\left[ {m\left( t \right)y\left( t \right) + p\left( t \right)y\left( {\tau \left( t \right)} \right)} \right]^\Delta } \right]^\Delta + q\left( t \right)f\left( {y\left( {\delta \left( t \right)} \right)} \right) = 0

Asymptotic properties of third order functional dynamic equations on time scales

on a time scale

Existence of solutions of the dynamic Cauchy problem on infinite time scale intervals

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