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Some notes on one oscillatory condition of neutral differential equations

Božena Mihalíková, Eva Chomová (2006)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The aim of this paper is to present sufficient conditions for all bounded solutions of the second order neutral differential equations of the form (r(t)(x(t) - px(t-τ))')' - q(t)f(x(σ(t))) = 0 to be oscillatory and to compare some existing results.

Some notes on oscillation of two-dimensional system of difference equations

Zdeněk Opluštil (2014)

Mathematica Bohemica

Oscillatory properties of solutions to the system of first-order linear difference equations Δ u k = q k v k Δ v k = - p k u k + 1 , are studied. It can be regarded as a discrete analogy of the linear Hamiltonian system of differential equations. We establish some new conditions, which provide oscillation of the considered system. Obtained results extend and improve, in certain sense, results presented in Opluštil (2011).

Some notes to existence and stability of the positive periodic solutions for a delayed nonlinear differential equations

Božena Dorociaková, Rudolf Olach (2016)

Open Mathematics

The paper deals with the existence of positive ω-periodic solutions for a class of nonlinear delay differential equations. For example, such equations represent the model for the survival of red blood cells in an animal. The sufficient conditions for the exponential stability of positive ω-periodic solution are also considered.

Some observations on a Conti's result

Adrian Constantin (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

An extension of a result of R. Conti is given from which some integro-differential inequalities of the Gronwall-Bellman-Bihari type and a criterion for the continuation of solutions of a system of ordinary differential equations are deduced.

Some oscillation theorems for second order differential equations

Chung-Fen Lee, Cheh Chih Yeh, Chuen-Yu Gau (2005)

Czechoslovak Mathematical Journal

In this paper we establish some oscillation or nonoscillation criteria for the second order half-linear differential equation ( r ( t ) Φ ( u ' ( t ) ) ) ' + c ( t ) Φ ( u ( t ) ) = 0 , where (i) r , c C ( [ t 0 , ) , : = ( - , ) ) and r ( t ) > 0 on [ t 0 , ) for some t 0 0 ; (ii) Φ ( u ) = | u | p - 2 u for some fixed number p > 1 . We also generalize some results of Hille-Wintner, Leighton and Willet.

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