An Analytic Solution for a Vasicek Interest Rate Convertible Bond Model by A. S. Deakin, Matt Davison

“…This paper provides the analytic solution to the partial differential equation for the value of a convertible bond. …”
Get full text

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.…”
Get full text

Existence and uniqueness theorems for some fourth-order nonlinear boundary value problems by Ruyun Ma

“…This paper is concerned with the problems of existence and uniqueness of solutions for the nonlinear fourth-order ordinary differential equation y′′′′+λy′′+ky+G(x,y,y′,y′′,y′′′)=f(x,y,y′,y′′,y′′′) with one of a particular set of boundary conditions.…”
Get full text

A New Result for ψ-Hilfer Fractional Pantograph-Type Langevin Equation and Inclusions by Hamid Lmou, Khalid Hilal, Ahmed Kajouni

“…In this paper, we deal with the existence and uniqueness of solution for ψ-Hilfer Langevin fractional pantograph differential equation and inclusion; these types of pantograph equations are a special class of delay differential equations. …”
Get full text

A New Proof of Central Limit Theorem for i.i.d. Random Variables by Zhaojun Zong, Feng Hu

“…Our main tool is the viscosity solution theory of partial differential equation (PDE).…”
Get full text

Existence and Nonexistence of Positive Solutions for Fractional Three-Point Boundary Value Problems with a Parameter by Yunhong Li, Weihua Jiang

“…In this work, we investigate the existence and nonexistence of positive solutions for p-Laplacian fractional differential equation with a parameter. On the basis of the properties of Green’s function and Guo-Krasnosel’skii fixed point theorem on cones, the existence and nonexistence of positive solutions are obtained for the boundary value problems. …”
Get full text

Moment Equations in Modeling a Stable Foreign Currency Exchange Market in Conditions of Uncertainty by Josef Diblík, Irada Dzhalladova, Mária Michalková, Miroslava Růžičková

“…The paper develops a mathematical model of foreign currency exchange market in the form of a stochastic linear differential equation with coefficients depending on a semi-Markov process. …”
Get full text

The Numerical Solution of the Bitsadze-Samarskii Nonlocal Boundary Value Problems with the Dirichlet-Neumann Condition by Allaberen Ashyralyev, Elif Ozturk

“…A procedure of modified Gauss elimination method is used for solving these difference schemes for the two-dimensional elliptic differential equation. The method is illustrated by numerical examples.…”
Get full text

On Extended b-Rectangular and Controlled Rectangular Fuzzy Metric-Like Spaces with Application by Naeem Saleem, Salman Furqan, Fahd Jarad

“…As an application, we utilize our main results to solve the uniqueness of the solution of a differential equation occurring in the dynamic market equilibrium.…”
Get full text

A Numerical Method for Lane-Emden Equations Using Hybrid Functions and the Collocation Method by Changqing Yang, Jianhua Hou

“…The collocation method transforms the differential equation into a system of algebraic equations. …”
Get full text

On Partial Complete Controllability of Semilinear Systems by Agamirza E. Bashirov, Maher Jneid

“…Many control systems can be written as a first-order differential equation if the state space enlarged. Therefore, general conditions on controllability, stated for the first-order differential equations, are too strong for these systems. …”
Get full text

Spatial Dynamics for a Generalized Solow Growth Model by Yue Zhong, Wenyi Huang

“…The explicit solutions of the growth model, which is expressed by a differential equation with corresponding boundary conditions, are employed to illustrate the spatial dynamics of the model in different economic regions. …”
Get full text

General Linear Boundary Value Problem for the Second-Order Integro-Differential Loaded Equation with Boundary Conditions Containing Both Nonlocal and Global Terms by M. R. Fatemi, N. A. Aliyev

“…The paper is devoted to obtaining the sufficient conditions for Fredholm property for the general boundary value problem of the second-order linear integro-differential equation. Here, the boundary conditions corresponding with the boundary value problem contain both nonlocal and global terms.…”
Get full text

The (G′/G)-Expansion Method and Its Application for Higher-Order Equations of KdV (III) by Huizhang Yang, Wei Li, Biyu Yang

“…New exact traveling wave solutions of a higher-order KdV equation type are studied by the (G′/G)-expansion method, where G=G(ξ) satisfies a second-order linear differential equation. The traveling wave solutions are expressed by the hyperbolic functions, the trigonometric functions, and the rational functions. …”
Get full text

Pulsation Calculation of Cylindrical Underwater Gas Explosion Products in Well by A. M. Sheiko, V. V. Ivashechkin, V. V. Veremenuk

“…The paper considers a mathematical model of pulsation process of cylindrical underwater gas explosion products in the well at gas-impulse regeneration filters. A differential equation of the second-order with constant coefficients has been derived. …”
Get full text

Some Results on Equivalence Groups by J. C. Ndogmo

“…The comparison of two common types of equivalence groups of differential equations is discussed, and it is shown that one type can be identified with a subgroup of the other type, and a case where the two groups are isomorphic is exhibited. …”
Get full text

The Role of Numerical Methods in the Sensitivity Analysis of a Density Parameter in a Passivation Rate Interaction by EN Ekaka-a, EO Chukwuocha, NM Nafo

“…The mathematical modelling of physiochemical interaction in the framework of industrial and environmental physics which relies on an initial value problem is defined by a first order ordinary differential equation. Two numerical methods of studying sensitivity analysis of physiochemical interaction data are developed. …”
Get full text

Necessary and Sufficient Conditions of Optimality for a Damped Hyperbolic Equation in One-Space Dimension by Ismail Kucuk, Kenan Yildirim

“…The present paper deals with the necessary optimality condition for a class of distributed parameter systems in which the system is modeled in one-space dimension by a hyperbolic partial differential equation subject to the damping and mixed constraints on state and controls. …”
Get full text

Stability of a Three-Species Cooperative System with Time Delays and Stochastic Perturbations by Jinxing Zhao, Yuanfu Shao

“…We establish the sufficient criteria of the asymptotical stability and stability in probability by constructing a neutral stochastic differential equation and some suitable functionals. The impacts of time delays and stochastic perturbations to the system dynamics are revealed by some numerical simulations at the end.…”
Get full text

An oriented coincidence index for nonlinear Fredholm inclusions with nonconvex-valued perturbations by Valeri Obukhovskii, Pietro Zecca, Victor Zvyagin

“…An example arising in the study of a mixed system, consisting of a first-order implicit differential equation and a differential inclusion, is given.…”
Get full text