Existence of positive periodic solutions to -species nonautonomous food chains with harvesting terms.
Existence of a nonautonomous SIR epidemic model with age structure.
Existence of almost periodic solutions for Hopfield neural networks with continuously distributed delays and impulses.
Existence of blow-up solutions for a degenerate parabolic-elliptic Keller–Segel system with logistic source
This paper deals with existence of finite-time blow-up solutions to a degenerate parabolic–elliptic Keller–Segel system with logistic source. Recently, finite-time blow-up was established for a degenerate Jäger–Luckhaus system with logistic source. However, blow-up solutions of the aforementioned system have not been obtained. The purpose of this paper is to construct blow-up solutions of a degenerate Keller–Segel system with logistic source.
Existence of global solution and nontrivial steady states for a system modeling chemotaxis.
Existence of global solutions for a predator-prey model with cross-diffusion.
Existence of global solutions for a system of reaction-diffusion equations having a triangular matrix.
Existence of limit cycles in a predator-prey system with a functional response.
Existence of periodic solutions for a delayed ratio-dependent three-species predator-prey diffusion system on time scales.
Existence of periodic solutions of a delayed predator-prey system on time scales.
Existence of positive periodic solutions for a class of nonautonomous difference equations.
Existence of positive periodic solutions for delayed predator-prey patch systems with stocking.
Existence of positive periodic solutions of an SEIR model with periodic coefficients
An SEIR model with periodic coefficients in epidemiology is considered. The global existence of periodic solutions with strictly positive components for this model is established by using the method of coincidence degree. Furthermore, a sufficient condition for the global stability of this model is obtained. An example based on the transmission of respiratory syncytial virus (RSV) is included.
Existence of Solutions for the Keller-Segel Model of Chemotaxis with Measures as Initial Data
A simple proof of the existence of solutions for the two-dimensional Keller-Segel model with measures with all the atoms less than 8π as the initial data is given. This result was obtained by Senba and Suzuki (2002) and Bedrossian and Masmoudi (2014) using different arguments. Moreover, we show a uniform bound for the existence time of solutions as well as an optimal hypercontractivity estimate.
Existence of solutions to generalized von Foerster equations with functional dependence
We prove the existence of solutions to a differential-functional system which describes a wide class of multi-component populations dependent on their past time and state densities and on their total size. Using two different types of the Hale operator, we incorporate in this model classical von Foerster-type equations as well as delays (past time dependence) and integrals (e.g. influence of a group of species).
Existence of Waves for a Nonlocal Reaction-Diffusion Equation
In this work we study a nonlocal reaction-diffusion equation arising in population dynamics. The integral term in the nonlinearity describes nonlocal stimulation of reproduction. We prove existence of travelling wave solutions by the Leray-Schauder method using topological degree for Fredholm and proper operators and special a priori estimates of solutions in weighted Hölder spaces.
Existence, uniqueness and ergodicity of positive solution of mutualism system with stochastic perturbation.
Existence, uniqueness and global asymptotic stability for a class of complex-valued neutral-type neural networks with time delays
This paper explores the problem of delay-independent and delay-dependent stability for a class of complex-valued neutral-type neural networks with time delays. Aiming at the neutral-type neural networks, an appropriate function is constructed to derive the existence of equilibrium point. On the basis of homeomorphism theory, Lyapunov functional method and linear matrix inequality techniques, several LMI-based sufficient conditions on the existence, uniqueness and global asymptotic stability of equilibrium...
Existence, uniqueness, approxiniate solutions construction and errors valuation theorems concerning mixed structure mathematical systems which generalizate the normal functioning of a single nerve equations.
Exp-function method for solving Huxley equation.