Variable Step Size Adams Methods for BSDEs by Qiang Han

“…For backward stochastic differential equations (BSDEs), we construct variable step size Adams methods by means of Itô–Taylor expansion, and these schemes are nonlinear multistep schemes. It is deduced that the conditions of local truncation errors with respect to Y and Z reach high order. …”
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Leray–Schauder Fixed Point Theorems for Block Operator Matrix with an Application by Mohamed Amine Farid, El Miloudi Marhrani, Mohamed Aamri

“…We will also prove the existence of solutions for a coupled system of nonlinear equations with an example.…”
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Fixed Point Theorems of Superlinear Operators with Applications by Shaoyuan Xu, Yan Han

“…The results are applied to nonlinear integral equations and partial differential equations.…”
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Existence and Uniqueness of Positive Solution for a Boundary Value Problem of Fractional Order by J. Caballero, J. Harjani, K. Sadarangani

“…We are concerned with the existence and uniqueness of positive solutions for the following nonlinear fractional boundary value problem: D0+αu(t)+f(t,u(t))=0, 0≤t≤1, 3<α≤4, u(0)=u′(0)=u″(0)=u″(1)=0, where D0+α denotes the standard Riemann-Liouville fractional derivative. …”
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Large diffusivity finite-dimensional asymptotic behaviour of a semilinear wave equation by Robert Willie

“…In the semilinear case, under suitable dissipative assumptions on the nonlinear term, we prove the existence of a global attractor for fixed diffusion and that the limiting attractor for large diffusion is finite dimensional.…”
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On a New Reliable Algorithm by A. K. Alomari, M. S. M. Noorani, R. Nazar

“…Comparisons between the MSHAM solutions and the fourth-order Runge-Kutta (RK4) numerical solutions reveal that the new technique is a promising tool for the nonlinear systems of ordinary differential equations.…”
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Capturing the Data Uncertainty Change in the Cocaine Consumption in Spain Using an Epidemiologically Based Model by Christopher Anaya, Clara Burgos, Juan-Carlos Cortés, Rafael-J. Villanueva

“…The proposed model is formulated through a nonlinear system of difference equations whose coefficients are treated as stochastic processes. …”
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A Numerical Method for Delayed Fractional-Order Differential Equations by Zhen Wang

“…A numerical method for nonlinear fractional-order differential equations with constant or time-varying delay is devised. …”
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Mapping error in the parallel realizations of SAMANN algorithm by Viktor Medvedev, Gintautas Dzemyda

“…We investigate an unsupervised back-propagation algorithm to train a multilayer feed-forward neural network (SAMANN) to perform the Sammoil's nonlinear projection and propose a parallel algorithm for SAMANN network.   …”
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Analytical Analysis of Fractional-Order Physical Models via a Caputo-Fabrizio Operator by Fatemah Mofarreh, A. M. Zidan, Muhammad Naeem, Rasool Shah, Roman Ullah, Kamsing Nonlaopon

“…Furthermore, due to the straightforward implementation, the proposed method can solve other nonlinear fractional-order problems.…”
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Existence of Solutions for Riemann-Liouville Fractional Boundary Value Problem by Wenzhe Xie, Jing Xiao, Zhiguo Luo

“…By using the method of upper and lower solutions and fixed point theorems, the existence of solutions for a Riemann-Liouville fractional boundary value problem with the nonlinear term depending on fractional derivative of lower order is obtained under the classical Nagumo conditions. …”
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Stability Analysis for Travelling Wave Solutions of the Olver and Fifth-Order KdV Equations by A. R. Seadawy, W. Amer, A. Sayed

“…Moreover, the methods can be applied to a wide class of nonlinear evolution equations. All solutions are exact and stable and have applications in physics.…”
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A Fractional Trust Region Method for Linear Equality Constrained Optimization by Honglan Zhu, Qin Ni, Liwei Zhang, Weiwei Yang

“…These results give the base of further research on nonlinear optimization.…”
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Global Existence and Asymptotic Behavior of Solutions for Compressible Two-Fluid Euler–Maxwell Equation by Ismahan Binshati, Harumi Hattori

“…Moreover, we use the result for Lp−Lq estimates to prove the decay rates for the nonlinear systems.…”
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A Generalized Nonuniform Contraction and Lyapunov Function by Fang-fang Liao, Yongxin Jiang, Zhiting Xie

“…Moreover, we show that the stability of a nonuniform contraction persists under sufficiently small nonlinear perturbations.…”
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Viability Discrimination of a Class of Control Systems on a Nonsmooth Region by Na Zhao, Jianfeng Lv, Jinlin Yang, Xinzhi Liu

“…In this paper, we consider the viability for both an affine nonlinear hybrid system and a hybrid differential inclusion on a region with subdifferentiable boundary. …”
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A Newton-type method and its application by V. Antony Vijesh, P. V. Subrahmanyam

“…We further obtain an existence theorem for a class of nonlinear functional integral equations involving the Urysohn operator.…”
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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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Operating with External Arguments of Douady and Hubbard by G. Pastor, M. Romera, G. Alvarez, J. Nunez, D. Arroyo, F. Montoya

“…The external arguments of the external rays theory of Douady and Hubbard is a valuable tool in order to analyze the Mandelbrot set, a typical case of discrete dynamical system used to study nonlinear phenomena. We suggest here a general method for the calculation of the external arguments of external rays landing at the hyperbolic components root points of the Mandelbrot set. …”
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Bogdanov-Takens and Triple Zero Bifurcations of a Delayed Modified Leslie-Gower Predator Prey System by Xia Liu, Jinling Wang

“…A delayed modified Leslie-Gower predator prey system with nonlinear harvesting is considered. The existence conditions that an equilibrium is Bogdanov-Takens (BT) or triple zero singularity of the system are given. …”
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