On a class of fourth order half-linear differential equations
Oscillation of a logistic equation with delay and diffusion
This paper establishes oscillation theorems for a class of functional parabolic equations which arises from logistic population models with delays and diffusion.
Linearized comparison criteria for a nonlinear neutral differential equation
A class of nonlinear neutral differential equations with variable coefficients and delays is considered. Conditions for the existence of eventually positive solutions are obtained which extend some of the criteria existing in the literature. In particular, a linearized comparison theorem is obtained which establishes a connection between our nonlinear equations and a class of linear neutral equations with constant coefficients.
Nota sobre un sistema compartimentado con retrasos.
Mean stability of a stochastic difference equation
A simple personal saving model with interest rate based on random fluctuation of national growth rate is considered. We establish connections between the mean stochastic stability of our model and the deterministic stability of related partial difference equations. Then the asymptotic behavior of our stochastic model is studied. Although the model is simple, the techniques for obtaining its properties are not, and we make use of the theory of abstract Banach algebras and weighted spaces. It is hoped...
Periodic solutions of nth order delay Rayleigh equations
A priori bounds are established for periodic solutions of an nth order Rayleigh equation with delay. From these bounds, existence theorems for periodic solutions are established by means of Mawhin's continuation theorem.
Kamenev type oscillation criteria for second order matrix differential systems with damping
By using monotone functionals and positive linear functionals on a suitable matrix space, new oscillation criteria for second order self-adjoint matrix differential systems with damping are given. The results are extensions of the Kamenev type oscillation criteria obtained by Wong for second order self-adjoint matrix differential systems with damping. These extensions also include an earlier result of Erbe et al.
Eventually positive solutions for nonlinear impulsive differential equations with delays
Several recent oscillation criteria are obtained for nonlinear delay impulsive differential equations by relating them to linear delay impulsive differential equations or inequalities, and then comparison and oscillation criteria for the latter are applied. However, not all nonlinear delay impulsive differential equations can be directly related to linear delay impulsive differential equations or inequalities. Moreover, standard oscillation criteria for linear equations cannot be applied directly...
Oscillation theorems for certain even order neutral differential equations
This paper is concerned with a class of even order nonlinear differential equations of the form where is even and . By using the generalized Riccati transformation and the averaging technique, new oscillation criteria are obtained which are either extensions of or complementary to a number of existing results. Our results are more general and sharper than some previous results even for second order equations.
Even periodic solutions of higher order duffing differential equations
By using Mawhin’s continuation theorem, the existence of even solutions with minimum positive period for a class of higher order nonlinear Duffing differential equations is studied.
Kamenev type oscillation criteria for nonlinear difference equations
By means of Riccati transformation techniques, we establish some new oscillation criteria for second-order nonlinear difference equation which are sharp.
Positive fixed point theorems arising from seeking steady states of neural networks
Biological systems are able to switch their neural systems into inhibitory states and it is therefore important to build mathematical models that can explain such phenomena. If we interpret such inhibitory modes as `positive' or `negative' steady states of neural networks, then we will need to find the corresponding fixed points. This paper shows positive fixed point theorems for a particular class of cellular neural networks whose neuron units are placed at the vertices of a regular polygon. The...
Existence and uniqueness of positive periodic solutions for a class of integral equations with parameters
Existence of periodic solutions of functional differential equations with parameters such as Nicholson’s blowflies model call for the investigation of integral equations with parameters defined over spaces with periodic structures. In this paper, we study one such equation , x ∈ Ω, by means of the proper value theory of operators in Banach spaces with cones. Existence, uniqueness and continuous dependence of proper solutions are established.
Periodic solutions for a neutral functional differential equation with multiple variable lags
By means of the Krasnoselskii fixed piont theorem, periodic solutions are found for a neutral type delay differential system of the form
Optimal sublinear inequalities involving geometric and power means
There are many relations involving the geometric means and power means for positive -vectors . Some of them assume the form of inequalities involving parameters. There then is the question of sharpness, which is quite difficult in general. In this paper we are concerned with inequalities of the form and with parameters and We obtain a necessary and sufficient condition for the former inequality, and a sharp condition for the latter. Several applications of our results are also demonstrated....
On a class of fourth order linear recurrence equations.
Sturmian theorems for components of coupled elliptic systems
Stability of a time discrete perturbed dynamical systems with delay.
An oscillation theorem for higher order nonhomogeneous superlinear differential equations.
Oscillation of second-order half-linear differential equations with dampling.
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