Existence and Uniqueness of Solution to Nonlinear Boundary Value Problems with Sign-Changing Green’s Function by Peiguo Zhang, Lishan Liu, Yonghong Wu

“…By using the cone theory and the Banach contraction mapping principle, the existence and uniqueness results are established for nonlinear higher-order differential equation boundary value problems with sign-changing Green’s function. …”
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Viscosity Solutions and American Option Pricing in a Stochastic Volatility Model of the Ornstein-Uhlenbeck Type by Alexandre F. Roch

“…We characterize the value of such derivatives as the unique viscosity solution of an integral-partial differential equation when the payoff function satisfies a Lipschitz condition.…”
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Existence of periodic traveling wave solution to the forced generalized nearly concentric Korteweg-de Vries equation by Kenneth L. Jones, Xiaogui He, Yunkai Chen

“…An equivalent relationship between the ordinary differential equation and nonlinear integral equations with symmetric kernels is established by using the Green's function method. …”
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Nonlinear Decomposition of Doob-Meyer's Type for Continuous g-Supermartingale with Uniformly Continuous Coefficient by Xuejun Shi, Long Jiang, Ronglin Ji

“…We prove that a continuous g-supermartingale with uniformly continuous coeffcient g on finite or infinite horizon, is a g-supersolution of the corresponding backward stochastic differential equation. It is a new nonlinear Doob-Meyer decomposition theorem for the g-supermartingale with continuous trajectory.…”
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Breather Wave Solutions and Interaction Solutions for Two Mixed Calogero-Bogoyavlenskii-Schiff and Bogoyavlensky-Konopelchenko Equations by Hongcai Ma, Caoyin Zhang, Aiping Deng

“…In this paper, based on a bilinear differential equation, we study the breather wave solutions by employing the extended homoclinic test method. …”
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On oscillation of a food-limited population model with time delay by Leonid Berezansky, Elena Braverman

“…For a scalar nonlinear delay differential equation Ṅ(t) = r(t)N(t)(K − N(h(t)))/(K + s(t)N(g(t))),r(t) ≥ 0, h(t) ≤ t, g(t) ≤ t and some generalizations of this equation, we establish explicit oscillation and nonoscillation conditions. …”
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On Oscillations of Solutions of Third-Order Dynamic Equation by Gro Hovhannisyan

“…We are proving the new oscillation theorems for the solutions of third-order linear nonautonomous differential equation with complex coefficients. In the case of real coefficients we derive the oscillation criterion that is invariant with respect to the adjoint transformation. …”
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A Novel Analytical Technique to Obtain Kink Solutions for Higher Order Nonlinear Fractional Evolution Equations by Qazi Mahmood Ul Hassan, Jamshad Ahmad, Muhammad Shakeel

“…A generalized fractional complex transform is appropriately used to convert this equation to ordinary differential equation which subsequently resulted in a number of exact solutions.…”
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RESEARCH CONCAVE CIRCULAR HOLE TEMPLATE LINEAR VARIABLE THICKNESS STIFFNESS AND STRENGTH THEORIES by LI ShaoJie

“…This paper studies linear variable thickness circular aperture concave template theory of stiffness and strength calculation.First,set up mechanical model:Template for circular concave,outside the perimeter fixed; center has a round hole,inside the perimeter free,outside under uniformly distributed vertical load.Secondly,the establishment of mathematical model:Derivation of concave template in the axisymmetric condition,ordinary differential equation with variable coefficients of elastic curved surface,and gives the mathematical expressions of boundary conditions.Again,in view of the differential equation boundary value problem,the displacement method and the Matlab algorithm,it is concluded that the deflection of concave template function,and establish the stiffness calculation condition of concave template.Then,determine the concave template on the bending moment and the maximum bending moment and stress,so as to establish a concave template strength calculation conditions.Finally,numerical examples.This paper presents the function solutions,to change law of control concave template section variable parameters.In this way,not only highlight the interdependent relationship between the quantity of each,and optimization,and discussion and application.The result is suitable for uniform,continuous,isotropic material artifacts.Because in the process of calculation and data processing with error,so the formula is similar.…”
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A New Approach for a Class of the Blasius Problem via a Transformation and Adomian’s Method by Abdelhalim Ebaid, Nwaf Al-Armani

“…Accordingly, the original differential equation is transformed into a singular differential equation with classical boundary conditions. …”
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Research on Stability of Explicit Runge-Kutta Method for Solving Constantly Gradually Varied Flow in Open Trough by ZHOU Bin

“…Explicit Runge-Kutta method is one of the commonly used algorithms to solve the differential equation of constantly gradually varied flow in open channel, which has been studied and popularized by some domestic scholars in recent years. …”
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Approximation for Transient of Nonlinear Circuits Using RHPM and BPES Methods by H. Vazquez-Leal, K. Boubaker, L. Hernandez-Martinez, J. Huerta-Chua

“…Therefore, in this paper, rational homotopy perturbation method and Boubaker Polynomials Expansion Scheme are applied to a differential equation from a nonlinear circuit. Comparing the results obtained by both techniques revealed that they are effective and convenient.…”
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Existence of Unbounded Solutions for a Third-Order Boundary Value Problem on Infinite Intervals by Hairong Lian, Junfang Zhao

“…We generalize the unbounded upper and lower solution method to a third-order ordinary differential equation on the half line subject to the Sturm-Liouville boundary conditions. …”
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Approximation Solutions for Local Fractional Schrödinger Equation in the One-Dimensional Cantorian System by Yang Zhao, De-Fu Cheng, Xiao-Jun Yang

“…The obtained solutions show that the present method is an efficient and simple tool for solving the linear partial differentiable equations within the local fractional derivative.…”
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Noether symmetries, solutions and conserved quantities of a new (3+1)-dimensional Painlevé integrable fifth-order equation with third-order temporal dispersion: Multi-analytical ap... by Oke Davies Adeyemo

“…In addition, the equation is reduced to its corresponding nonlinear ordinary differential equation using a plane wave transformation. …”
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Coefficient Bounds for Certain Subclasses of Analytic Functions Defined by Komatu Integral Operator by Serap Bulut

“…We determine the coeffcient bounds for functions in certain subclasses of analytic functions of complex order, which are introduced here by means of a certain non-homogeneous Cauchy–Euler type differential equation of order m. Relevant connections of some of the results obtained with those in earlier works are also provided.…”
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The Second Kummer Function with Matrix Parameters and Its Asymptotic Behaviour by Georg Wehowar, Erika Hausenblas

“…Further, we provide a closed form of a solution of a Weber matrix differential equation and give a representation using the second Kummer function.…”
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CONTROL PROBLEMS FOR NONLINEAR VARIATIONAL EVOLUTION INEQUALITIES by Su Jin Cheon

“…In this paper, we deal with the approximate control-ability for the nonlinear functional differential equation governed by the variational inequality in Hilbert spaces and present a general theorems under which previous results easily follow. …”
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Positive Solutions of a Fractional Boundary Value Problem with Changing Sign Nonlinearity by Yongqing Wang, Lishan Liu, Yonghong Wu

“…We discuss the existence of positive solutions of a boundary value problem of nonlinear fractional differential equation with changing sign nonlinearity. We first derive some properties of the associated Green function and then obtain some results on the existence of positive solutions by means of the Krasnoselskii's fixed point theorem in a cone.…”
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Nonlinear Dynamic Analysis of the Cutting Process of a Nonextensible Composite Boring Bar by Bole Ma, Yongsheng Ren

“…The motion equation of nonlinear chatter of the cutting system is derived based on the Hamilton principle. The partial differential equation of motion is discretized using the Galerkin method to obtain a 1-dof nonlinear ordinary differential equation in a generalized coordinate system. …”
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