Input-to-State Stability of Singularly Perturbed Control Systems with Delays by Yongxiang Zhao, Aiguo Xiao, Li Li

“…By using the generalized Halanay inequality and Lyapunov functions, we derive the input-to-state stability of some classes of linear and nonlinear singularly perturbed control systems with delays.…”
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Investigating a Class of Generalized Caputo-Type Fractional Integro-Differential Equations by Saeed M. Ali, Wasfi Shatanawi, Mohammed D. Kassim, Mohammed S. Abdo, S. Saleh

“…In this article, we prove some new uniqueness and Ulam-Hyers stability results of a nonlinear generalized fractional integro-differential equation in the frame of Caputo derivative involving a new kernel in terms of another function ψ. …”
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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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Some New Coupled Coincidence Point and Coupled Fixed Point Results in Partially Ordered Metric-Like Spaces and an Application by Min Liang, Chuanxi Zhu, Zhaoqi Wu, Chunfang Chen

“…As an application, we discuss the existence of the solutions for a class of nonlinear integral equations.…”
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Application of the Homotopy Analysis Method for Solving the Variable Coefficient KdV-Burgers Equation by Dianchen Lu, Jie Liu

“…The results indicate that this method is efficient for the nonlinear models with the dissipative terms and variable coefficients.…”
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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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A graphical exploration of the relationship between parasite aggregation indices. by R McVinish, R J G Lester

“…The contour plots highlight the nonlinear nature of the relationships between these measures and suggest that correlations are not a suitable summary of these relationships.…”
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Chaotic Characteristic Verification of Gearbox Vibration Signal based on the Time Synchronous Averaging and Separation Technology by Li Jie, Zhao Jianmin

“…The gearbox vibration signal of normal and different degrees teeth break fault condition are analyzed,the chaotic characteristics of the gearbox vibration signal are verified by using the time synchronous averaging method（ TSA） to separate the linear components in the vibration signal of the gearbox and the remaining nonlinear components as the research object. The results show,the chaotic characteristic of gearbox degeneration can be effectively extracted,the existence of chaos in the vibration signal of gearbox is verified in the life-time run.…”
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On the Initial Value Problem of Stochastic Evolution Equations in Hilbert Spaces by Xuping Zhang, Yongxiang Li, Pengyu Chen

“…The existence of saturated mild solution and global mild solution is obtained under the situation that the nonlinear term satisfies some appropriate growth conditions. …”
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Painlevé Analysis, Soliton Molecule, and Lump Solution of the Higher-Order Boussinesq Equation by Bo Ren

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On the solvability of a higher-order semilinear ODE by Cristian-Paul Danet

“…The last result is stated when the nonlinearity has asymptotic behaviour at both infinity and zero.…”
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Fractional Langevin Equations with Nonseparated Integral Boundary Conditions by Khalid Hilal, Lahcen Ibnelazyz, Karim Guida, Said Melliani

“…In this paper, we discuss the existence of solutions for nonlinear fractional Langevin equations with nonseparated type integral boundary conditions. …”
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Fractional-Order Sliding Mode Synchronization for Fractional-Order Chaotic Systems by Chenhui Wang

“…Some sufficient conditions, which are valid for stability check of fractional-order nonlinear systems, are given in this paper. Based on these results, the synchronization of two fractional-order chaotic systems is investigated. …”
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Upper and Lower Solutions for m-Point Impulsive BVP with One-Dimensional p-Laplacian by Junfang Zhao, Jianfeng Zhao, Weigao Ge

“…Nagumo conditions play an important role in the nonlinear term involved with the first-order derivatives.…”
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Existence and Multiplicity of Solutions to Discrete Conjugate Boundary Value Problems by Bo Zheng

“…A generalized asymptotically linear condition on the nonlinearity is proposed, which includes the asymptotically linear as a special case. …”
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Optimization of the learning rate in the algorithm for data visualization by Viktor Medvedev, Gintautas Dzemyda

“…The paper describes an unsupervised backpropagation algorithm to train a multilayer feed-forward neural network (SAMANN) to perform the Sammon‘s nonlinear projection. In our research the emphasis is put on the optimization of the learning rate to save computation time without losing the mapping quality. …”
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Renormalization group analysis for thermal turbulence by D. N. Riahi

“…Turbulent fluxes for the flow are accounted for by repeatedly recasting the governing equations with the smallest scales represented by effective larger scales. Expressions for nonlinear contributions to eddy viscosity and eddy diffusivity are determined, and leading order contributions due to buoyancy on various results and equations are estimated. …”
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A Theoretical Analysis of Frequency Multipliers of the Step Recovery Diode in the Shunt-Mode of Operation by Wei Zonglu

“…Frequency multipliers of arbitrary nonlinear capacitor with an idler are generally considered, and explicit and useful formulae are given. …”
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Propagation of Water Waves over Uneven Bottom under the Effect of Surface Tension by Juan Carlos Muñoz Grajales

“…We establish existence and uniqueness of solutions to the Cauchy problem associated with a new one-dimensional weakly-nonlinear, weakly-dispersive system which arises as an asymptotical approximation of the full potential theory equations for modelling propagation of small amplitude water waves on the surface of a shallow channel with variable depth, taking into account the effect of surface tension. …”
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Locally Lipschitz Composition Operators in Space of the Functions of Bounded κΦ-Variation by Odalis Mejía, Nelson José Merentes Díaz, Beata Rzepka

“…We give a necessary and sufficient condition on a function h:R→R under which the nonlinear composition operator H, associated with the function h, Hu(t)=h(u(t)), acts in the space κΦBV[a,b] and satisfies a local Lipschitz condition.…”
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