The shallow water equations: conservation laws and symplectic geometry by Yilmaz Akyildiz

“…We consider the system of nonlinear differential equations governing shallow water waves over a uniform or sloping bottom. …”
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Fixed Point Theorems and Uniqueness of the Periodic Solution for the Hematopoiesis Models by Jun Wu, Yicheng Liu

“…We present some results to the existence and uniqueness of the periodic solutions for the hematopoiesis models which are described by the functional differential equations with multiple delays. Our methods are based on the equivalent norm techniques and a new fixed point theorem in the continuous function space.…”
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Existence and Uniqueness Theorems of Ordered Contractive Map in Banach Lattices by Xingchang Li, Zhihao Wang

“…Moreover, we prove the existence of a unique solution for first-order ordinary differential equations with initial value conditions by using the theoretical results with no need for using the condition of a lower solution or an upper solution.…”
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Poincaré Bifurcations of Two Classes of Polynomial Systems by Jing Wang, Shuliang Shui

“…Using bifurcation methods and the Abelian integral, we investigate the number of the limit cycles that bifurcate from the period annulus of the singular point when we perturb the planar ordinary differential equations of the form , with an arbitrary polynomial vector field, where or .…”
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In Search of Chaos in Genetic Systems by Felix Sadyrbaev, Olga Kozlovska

“…A three-dimensional multiparametric system of ordinary differential equations, arising in the theory of genetic networks, is considered. …”
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Substantiation of asymptotical solution of weakly nonlinear hyperbolic system by Aleksandras Krylovas

“… A hyperbolic system of first order partial differential equations with small parameter and periodical initial conditions is obtained. …”
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Controllability of semilinear stochastic delay evolution equations in Hilbert spaces by P. Balasubramaniam, J. P. Dauer

“…An application to stochastic partial differential equations is given.…”
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An Iterative Method for Time-Fractional Swift-Hohenberg Equation by Wenjin Li, Yanni Pang

“…Using this iterative method, we obtain the approximate analytic solutions with numerical figures to initial value problems, which indicates that such iterative method is effective and simple in constructing approximate solutions to Cauchy problems of time-fractional differential equations.…”
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Monotonic Limit Properties for Solutions of BSDEs with Continuous Coefficients by ShengJun Fan, Xing Song, Ming Ma

“…This paper investigates the monotonic limit properties for the minimal and maximal solutions of certain one-dimensional backward stochastic differential equations with continuous coefficients.…”
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Stratifications and foliations in phase portraits of gene network models by V. P. Golubyatnikov, A. A. Akinshin, N. B. Ayupova, L. S. Minushkina

“…Periodic processes of gene network functioning are described with good precision by periodic trajectories (limit cycles) of multidimensional systems of kinetic-type differential equations. In the literature, such systems are often called dynamical, they are composed according to schemes of positive and negative feedback between components of these networks. …”
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A comprehensive numerical study exploring the significance of thermally reactive bioconvection in Falkner-Skan flow of Williamson nanomaterials influenced by activation energy and... by M. Israr Ur Rehman, Haibo Chen, Aamir Hamid, Wu Qian, Refka Ghodhbani, Mohamed Hussien

“…Similarity transformations are used to convert the system of partial differential equations into a system of ordinary differential equations, which are then numerically solved using the Runge–Kutta–Fehlberg (RKF-45) method. …”
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C0-semigroups of linear operators on some ultrametric Banach spaces by Toka Diagana

“…As an illustration, we will discuss the solvability of some homogeneous p-adic differential equations.…”
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On the stability of the linear delay differential and difference equations by A. Ashyralyev, P. E. Sobolevskii

“…We consider the initial-value problem for linear delay partial differential equations of the parabolic type. We give a sufficient condition for the stability of the solution of this initial-value problem. …”
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The Yang-Laplace Transform for Solving the IVPs with Local Fractional Derivative by Chun-Guang Zhao, Ai-Min Yang, Hossein Jafari, Ahmad Haghbin

“…Analytical solutions for the homogeneous and nonhomogeneous local fractional differential equations are discussed by using the Yang-Laplace transform.…”
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On Eigenvalues of the Generator of a C0-Semigroup Appearing in Queueing Theory by Geni Gupur

“…We describe the point spectrum of the generator of a C0-semigroup associated with the M/M/1 queueing model that is governed by an infinite system of partial differential equations with integral boundary conditions. …”
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Sociodynamics applied to the evolution of urban and regional structures by Wolfgang Weidlich

“…From it the set of nonlinear coupled differential equations for the quasi-meanvalues of the macrovariables can be derived.…”
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The Method of Coupled Fixed Points and Coupled Quasisolutions When Working with ODE’s with Arguments of Bounded Variation by Rubén Figueroa

“…The aim of this paper is to show the use of the coupled quasisolutions method as a useful technique when dealing with ordinary differential equations with functional arguments of bounded variation. …”
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Benjamin-Ono Equation on a Half-Line by Nakao Hayashi, Elena I. Kaikina

“…We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time.…”
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Hyperbolic differential-operator equations on a whole axis by Yakov Yakubov

“…Then we show applications of obtained abstract results to hyperbolic differential equations which, in particular, may represent the longitudinal displacements of an inhomogeneous rod under the action of forces at the two ends which are proportional to the acceleration.…”
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Building Infinitely Many Solutions for Some Model of Sublinear Multipoint Boundary Value Problems by Guy Aymard Degla

“…The idea of the proof is of independent interest since it shows a constructive way to have ordinary differential equations with multiple solutions.…”
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