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Oscillatory solutions of nonlinear fourth order differential equations with a middle term
We study oscillation of a fourth order nonlinear differential equation with a middle term. Using a certain energy function, we describe the properties of oscillatory solutions. The paper extendsExpand
On oscillatory solutions of quasilinear differential equations
Abstract Necessary and sufficient conditions for the existence of at least one oscillatory solution of a second-order quasilinear differential equation are presented. These results yield also newExpand
Asymptotics for higher order differential equations with a middle term.
Higher order nonlinear differential equations with the middle term as a perturbation of certain linear equations are studied. Using an iterative method, we show that for every solution of nonlinearExpand
On singular solutions of a second order differential equation
Sufficient conditions are given under which all nontrivial solutions of (g(a(t)y'))' + r(t)f(y) = 0 are proper where a > 0,r > 0, f(x)x>0 , g(x)x>0 for x is different from zero and g is increasing.AExpand
Asymptotic properties of oscillatory solutions of differential equations of the n-th order
Global structure and oscillatory criteria of the n-th order differential equation are investigated.
Remark on kneser problem
We study the existence of proper Kneser solutiolis of a systenl of differential equations. Especially, we remark how this result can be applied on a nonlinear differential equation withExpand
Oscillation of third order differential equation with damping term
We study asymptotic and oscillatory properties of solutions to the third order differential equation with a damping term $$x'''(t) + q(t)x'(t) + r(t)\left| x \right|^\lambda (t)\operatorname{sgn}Expand
On structure of solutions of a system of four differential inequalities
AbstractThe aim of the paper is to study a global structure of solutions of four differential inequalities $$\begin{gathered} \alpha _i y'_i (t)y_i + 1 \geqslant 0, y_i + 1(t) = 0 \Rightarrow y'_iExpand