Gluing for the Einstein constraint equations by Corvino, Justin

“…Initial data for the Einstein equations must satisfy a system of nonlinear partial differential equations, the Einstein constraint equations. …”
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Global Existence for the 3D Tropical Climate Model with Small Initial Data in H˙1/2ℝ3∗ by Hui Zhang, Juan Xu

“…The well-posedness problem is an important but challenging research topic in nonlinear partial differential equations. In this paper, we establish a global-in-time existence result of strong solutions for small initial data in terms of the H˙1/2ℝ3 norm on three-dimensional tropical climate model with viscosities by derive a blow-up criterion combine with energy estimates. …”
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Dynamic Properties of the Solow Model with Increasing or Decreasing Population and Time-to-Build Technology by Luca Guerrini, Mauro Sodini

“…The analytical results are obtained using the recent technique introduced by Beretta and Kuang (2002) in the studying of delayed differential equations with delay-dependent coefficients in characteristic equation. …”
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Dynamic Behaviors of an SEIR Epidemic Model in a Periodic Environment with Impulse Vaccination by Mei Yan, Zhongyi Xiang

“…By applying Floquet theory and the comparison theorem of impulsive differential equations, a threshold parameter which determines the extinction or persistence of the disease is presented. …”
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Skew Circulant Type Matrices Involving the Sum of Fibonacci and Lucas Numbers by Zhaolin Jiang, Yunlan Wei

“…Skew circulant and circulant matrices have been an ideal research area and hot issue for solving various differential equations. In this paper, the skew circulant type matrices with the sum of Fibonacci and Lucas numbers are discussed. …”
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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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Stability and Hopf Bifurcation in a Diffusive Predator-Prey System with Beddington-DeAngelis Functional Response and Time Delay by Yuzhen Bai, Xiaopeng Zhang

“…Finally, the direction and stability of Hopf bifurcations are determined by normal form theory and center manifold reduction for partial functional differential equations.…”
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On the Exact Solutions of Nonlinear Potential Yu–Toda–Sasa–Fukuyama Equation by Different Methods by Qinghao Zhu, Jianming Qi

“…It is observed that the extended complex method and G′/G-expansion method are reliable and will be used extensively to seek for exact solutions of any other nonlinear partial differential equations (NPDEs).…”
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Wavelet-Galerkin Quasilinearization Method for Nonlinear Boundary Value Problems by Umer Saeed, Mujeeb ur Rehman

“…Quasilinearization technique is applied to linearize the nonlinear differential equation and then wavelet-Galerkin method is implemented to linearized differential equations. …”
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Global stability for the prion equation with general incidence by Pierre Gabriel

“…We consider the so-called prion equation with the general incidence term introduced in [14], and we investigate the stability of the steady states.The method is based on the reduction technique introduced in [11].The argument combines a recent spectral gap result for the growth-fragmentation equation in weighted $L^1$ spaces and the analysis of a nonlinear system of three ordinary differential equations.…”
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Integral price formulas for lookback options by Chenglong Xu, Yue Kuen Kwok

“…The intricacies in the derivation procedures using the partial differential equation techniques stem from the degenerate nature of the pricing models, where the lookback state variables appear only in the auxiliary conditions but not in the governing differential equations. …”
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A therapy inactivating the tumor angiogenic factors by Cristian Morales-Rodrigo

“…This paper is devoted to a nonlinear system of partial differential equations modeling the effect of an anti-angiogenic therapy based on an agent that binds to the tumor angiogenic factors. …”
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On Stability of Nonautonomous Perturbed Semilinear Fractional Differential Systems of Order α∈(1,2) by Mohammed M. Matar, Esmail S. Abu Skhail

“…We study the Mittag-Leffler and class-K function stability of fractional differential equations with order α∈(1,2). We also investigate the comparison between two systems with Caputo and Riemann-Liouville derivatives. …”
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C⁎-Algebra-Valued G-Metric Spaces and Related Fixed-Point Theorems by Congcong Shen, Lining Jiang, Zhenhua Ma

“…As an application, we prove the existence and uniqueness of the solution of a type of differential equations.…”
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On a Partial q-Analog of a Singularly Perturbed Problem with Fuchsian and Irregular Time Singularities by Stephane Malek

“…A family of linear singularly perturbed difference differential equations is examined. These equations stand for an analog of singularly perturbed PDEs with irregular and Fuchsian singularities in the complex domain recently investigated by A. …”
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Nonlinear variational evolution inequalities in Hilbert spaces by Jin-Mun Jeong, Doo-Hoan Jeong, Jong-Yeoul Park

“…The regular problem for solutions of the nonlinear functional differential equations with a nonlinear hemicontinuous and coercive operator A and a nonlinear term f(.,.)…”
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Parametrically excited nonlinear systems: a comparison of two methods by A. F. El-Bassiouny

“…Two approximate methods (the multiple scales and the generalized synchronization) are used to construct a first-order nonlinear ordinary differential equations governing the modulation of the amplitudes and phases. …”
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Some Properties and Applications of a New General Triple Integral Transform “Gamar Transform’’ by Abdelilah Kamal H. Sedeeg

“…Moreover, the proposed new transform is applied to solve some partial differential equations (PDEs) such as Laplace, Mboctara, and Wave equations. …”
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Hilfer-Hadamard Nonlocal Integro-Multipoint Fractional Boundary Value Problems by Chanon Promsakon, Sotiris K. Ntouyas, Jessada Tariboon

“…This paper is concerned with the existence and uniqueness of solutions for a new class of boundary value problems, consisting by Hilfer-Hadamard fractional differential equations, supplemented with nonlocal integro-multipoint boundary conditions. …”
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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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