Topological structure of solution sets of differential inclusions: the constrained case by Wojciech Kryszewski

“…We survey and announce some current results on the existence, the viability, and the topological structure of the viable solutions of differential equations and inclusion in Banach spaces under set constraints. …”
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Asymptotic Solutions of Singular Perturbed Problems with an Instable Spectrum of the Limiting Operator by Burkhan T. Kalimbetov, Marat A. Temirbekov, Zhanibek O. Khabibullayev

“…The main idea of this method is based on the analysis of dual singular points of investigated equations and passage in the space of the larger dimension, what reduces to study of systems of first-order partial differential equations with incomplete initial data.…”
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Positive Periodic Solutions in a Discrete Time Three Species Competition System by Changjin Xu, Yusen Wu

“…With the aid of differential equations with piecewise constant arguments, a discrete analogue of continuous nonautonomous three species competition system is proposed. …”
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Explicit Determinants of the RFPrLrR Circulant and RLPrFrL Circulant Matrices Involving Some Famous Numbers by Tingting Xu, Zhaolin Jiang, Ziwu Jiang

“…Circulant matrices may play a crucial role in solving various differential equations. In this paper, the techniques used herein are based on the inverse factorization of polynomial. …”
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Bifurcation of Travelling Wave Solutions of the Generalized Zakharov Equation by Masoud Mosaddeghi

“…By using bifurcation theory of planar ordinary differential equations all different bounded travelling wave solutions of the generalized Zakharov equation are classified in to different parametric regions. …”
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Self-Similarity Analysis of the Nonlinear Schrödinger Equation in the Madelung Form by Imre F. Barna, Mihály A. Pocsai, L. Mátyás

“…The obtained system of differential equations is highly nonlinear. Regarding the solutions, a larger coefficient of the nonlinear term yields stronger deviation of the solution from the linear case.…”
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The Global Solutions and Moment Boundedness of Stochastic Multipantograph Equations by Maosheng Tian, Xuejing Meng, Jihong Chen, Xiaoqi Tang

“…Methods and techniques developed here have the potential to be applied in other unbounded delay stochastic differential equations.…”
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Local Fractional Laplace Variational Iteration Method for Fractal Vehicular Traffic Flow by Yang Li, Long-Fei Wang, Sheng-Da Zeng, Yang Zhao

“…We discuss the line partial differential equations arising in fractal vehicular traffic flow. …”
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Exact Determinants of Some Special Circulant Matrices Involving Four Kinds of Famous Numbers by Xiaoyu Jiang, Kicheon Hong

“…Circulant matrix family is used for modeling many problems arising in solving various differential equations. The RSFPLR circulant matrices and RSLPFL circulant matrices are two special circulant matrices. …”
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The Positive Role of Multiplicative Noise in Complete Synchronization of Unidirectionally Coupled Ring with Three Nodes by Yuzhu Xiao, Sufang Tang, Zhongkui Sun

“…Based on the theory of stochastic differential equations, we demonstrate that noise plays a positive role in complete synchronization. …”
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New Iterative Method for Fractional Gas Dynamics and Coupled Burger’s Equations by Mohamed S. Al-luhaibi

“…Numerical results show that the new iterative method is easy to implement and accurate when applied to time-fractional partial differential equations.…”
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Helmholtz and Diffusion Equations Associated with Local Fractional Derivative Operators Involving the Cantorian and Cantor-Type Cylindrical Coordinates by Ya-Juan Hao, H. M. Srivastava, Hossein Jafari, Xiao-Jun Yang

“…The Cantor-type cylindrical-coordinate method is applied to handle the corresponding local fractional differential equations. Two illustrative examples for the Helmholtz and diffusion equations on the Cantor sets are shown by making use of the Cantorian and Cantor-type cylindrical coordinates.…”
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Computable error bounds for collocation methods by A. H. Ahmed

“…This paper deals with error bounds for numerical solutions of linear ordinary differential equations by global or piecewise polynomial collocation methods which are based on consideration of the involved differential operator, related matrices and the residual. …”
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Approximate Solutions of Fractional Riccati Equations Using the Adomian Decomposition Method by Fei Wu, Lan-Lan Huang

“…In this paper, it was used to solve some fractional nonlinear differential equations.…”
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Numerical Method for a Markov-Modulated Risk Model with Two-Sided Jumps by Hua Dong, Xianghua Zhao

“…We first derive a system of differential equations for the Gerber-Shiu function. Furthermore, a numerical result is given based on Chebyshev polynomial approximation. …”
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Positive Solutions for p-Laplacian Fourth-Order Differential System with Integral Boundary Conditions by Jiqiang Jiang, Lishan Liu, Yonghong Wu

“…This paper investigates the existence of positive solutions for a class of singular p-Laplacian fourth-order differential equations with integral boundary conditions. …”
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Solution Properties of Linear Descriptor (Singular) Matrix Differential Systems of Higher Order with (Non-) Consistent Initial Conditions by Athanasios A. Pantelous, Athanasios D. Karageorgos, Grigoris I. Kalogeropoulos, Kostas G. Arvanitis

“…In some interesting applications in control and system theory, linear descriptor (singular) matrix differential equations of higher order with time-invariant coefficients and (non-) consistent initial conditions have been used. …”
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Analytic and Approximate Solutions of the Space-Time Fractional Schrödinger Equations by Homotopy Perturbation Sumudu Transform Method by Sara H. M. Hamed, Eltayeb A. Yousif, Arbab I. Arbab

“…The results show that the method is effective and convenient for solving nonlinear differential equations of fractional order.…”
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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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On the existence of classical solutions for differential-functional IBVP by Krzysztof A. Topolski

“…Our formulation and results cover a large class of parabolic problems both with a deviated argument and integro-differential equations.…”
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