Dichotomies with No Invariant Unstable Manifolds for Autonomous Equations by Răzvan O. Moşincat, Ciprian Preda, Petre Preda

“…We analyze the existence of (no past) exponential dichotomies for a well-posed autonomous differential equation (that generates a C0-semigroup {𝑇(𝑡)}𝑡≥0). …”
Get full text

Double Stratified Mixed Convective Flow of Couple Stress Nanofluid past Inclined Stretching Cylinder Using Cattaneo-Christov Heat and Mass Flux Model by Wubshet Ibrahim, Gosa Gadisa

“…The governing partial differential equation of the boundary layer flow region is reduced to its corresponding ordinary differential equation using a similarity transformation technique. …”
Get full text

Why Fuzzy Transform Is Efficient in Large-Scale Prediction Problems: A Theoretical Explanation by Irina Perfilieva, Vladik Kreinovich

“…Traditionally, to obtain such large-scale predictions, we first perform a detailed integration of the corresponding differential equation and then average the resulting detailed solution. …”
Get full text

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

The Local Stability of Solutions for a Nonlinear Equation by Haibo Yan, Ls Yong

“…The approach of Kruzkov’s device of doubling the variables is applied to establish the local stability of strong solutions for a nonlinear partial differential equation in the space L1(R) by assuming that the initial value only lies in the space L1(R)∩L∞(R).…”
Get full text

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. …”
Get full text

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.…”
Get full text

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. …”
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

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text

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. …”
Get full text

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.…”
Get full text

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.…”
Get full text

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. …”
Get full text

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.…”
Get full text

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.…”
Get full text

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. …”
Get full text

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.…”
Get full text