Frequency-Uniform Decomposition, Function Spaces , and Applications to Nonlinear Evolution Equations by Shaolei Ru, Jiecheng Chen

“…Moreover, we study the Cauchy problem for the generalized NLS equations and Ginzburg-Landau equations in .…”
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On Approximate Solutions of Functional Equations in Vector Lattices by Bogdan Batko

“…The main result will be applied to prove the stability of an alternative Cauchy functional equation F(x+y)+F(x)+F(y)≠0⇒F(x+y)=F(x)+F(y) in Riesz spaces, the Cauchy equation with squares F(x+y)2=(F(x)+F(y))2 in f-algebras, and the quadratic functional equation F(x+y)+F(x-y)=2F(x)+2F(y) in Riesz spaces.…”
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Existence and Attractivity for Fractional Evolution Equations by Yong Zhou, Jia Wei He, Bashir Ahmad, Ahmed Alsaedi

“…We establish sufficient conditions for the global attractivity of mild solutions for the Cauchy problems in the case that semigroup is compact.…”
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Gevrey Regularity for the Noncutoff Nonlinear Homogeneous Boltzmann Equation with Strong Singularity by Shi-you Lin

“…The Cauchy problem of the nonlinear spatially homogeneous Boltzmann equation without angular cutoff is studied. …”
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On a general Hyers-Ulam stability result by Costanz Borelli, Gian Luigi Forti

“…As particular cases we obtain many of the results published in the last ten years on the stability of the Cauchy and quadratic equation.…”
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Global Conservative Solutions of a Generalized Two-Component Camassa-Holm System by Feng Zhang, Han Yang, Yonghong Wu

“…The Cauchy problem for a generalized two-component Camassa-Holm system is investigated. …”
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Fixed Point Results in Quasi-Cone Metric Spaces by Fawzia Shaddad, Mohd Salmi Md Noorani

“…This is achieved by introducing different kinds of Cauchy sequences in quasi-cone metric spaces.…”
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Note on a -Contour Integral Formula of Gasper-Rahman by Jian-Ping Fang

“…We use the -Chu-Vandermonde formula and transformation technique to derive a more general -integral equation given by Gasper and Rahman, which involves the Cauchy polynomial. In addition, some applications of the general formula are presented in this paper.…”
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Solving a system of Caputo-Hadamard fractional differential equations via Perov’s fixed point theorem by Nouar Aziza Souad, Nisse Khadidja, Beloul Said

“…In this study, we discuss the existence and the uniqueness of the solution to Caputo-Hadamard Cauchy problems for a system of fractional differential equations, by using Perov’s fixed point theorem. …”
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Estimates for Unimodular Multipliers on Modulation Hardy Spaces by Jiecheng Chen, Dashan Fan, Lijing Sun, Chunjie Zhang

“…As applications, we give the grow-up rate of the solution for the Cauchy problems for the free Schrödinger equation with the initial data in a modulation space, as well as some mixed norm estimates. …”
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Preparing and Storing an Emergency Safe Drinking Water Supply by Andrea Albertin, Thomas Obreza

“…Original publication:  Shukla, Shuchi, and Thomas Obreza. 1. “Preparing and Storing an Emergency Safe Drinking Water Supply”. …”
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Preparing and Storing an Emergency Safe Drinking Water Supply by Andrea Albertin, Thomas Obreza

“…Original publication:  Shukla, Shuchi, and Thomas Obreza. 1. “Preparing and Storing an Emergency Safe Drinking Water Supply”. …”
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Klein-Gordon Equations on Modulation Spaces by Guoping Zhao, Jiecheng Chen, Weichao Guo

“…We consider the Cauchy problem for a family of Klein-Gordon equations with initial data in modulation spaces Mp,1a. …”
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A Challenge for Diagnosing Acute Liver Injury with Concomitant/Sequential Exposure to Multiple Drugs: Can Causality Assessment Scales Be Utilized to Identify the Offending Drug? by Roxanne Lim, Hassan Choudry, Kim Conner, Wikrom Karnsakul

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Second Order Impulsive Retarded Differential Inclusions with Nonlocal Conditions by Hernán R. Henríquez, Marcos Rabelo, Luciana Vale

“…In this work we establish some existence results for abstract second order Cauchy problems modeled by a retarded differential inclusion involving nonlocal and impulsive conditions. …”
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A Regularity Criterion for the Magneto-Micropolar Fluid Equations in B˙∞,∞−1 by Zhihao Tang, Gang Wang, Haiwa Guan

“…The paper is dedicated to study of the Cauchy problem for the magneto-micropolar fluid equations in three-dimensional spaces. …”
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On the Existence of Long-Time Classical Solutions for the 2D Inviscid Boussinesq Equations by Jiafa Xu, Lishan Liu

“…In this paper, we consider the Cauchy problem for the 2D inviscid Boussinesq equations with N being the buoyancy frequency. …”
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Refinement equations for generalized translations by W. Christopher Lang

“…We study refinement equations which relate the dilation of a function with generalized translates of the function, consisting of convolutions against certain kernels including Cauchy and Gaussian densities; solutions are expressed in terms of solutions of the corresponding refinement equation involving ordinary translation.…”
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Fractional Operators in p-adic Variable Exponent Lebesgue Spaces and Application to p-adic Derivative by Leonardo Fabio Chacón-Cortés, Humberto Rafeiro

“…As an application, we show the existence and uniqueness of the solution for a nonhomogeneous Cauchy problem in the p-adic variable exponent Lebesgue spaces.…”
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Uniform in Time Description for Weak Solutions of the Hopf Equation with Nonconvex Nonlinearity by Antonio Olivas Martinez, Georgy A. Omel'yanov

“…Applying the weak asymptotics method we construct a uniform in time description for the Cauchy data evolution and show that the use of this method implies automatically the appearance of the Oleinik E-condition.…”
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