Oscillation Properties for Second-Order Partial Differential Equations with Damping and Functional Arguments by Run Xu, Yuhua Lu, Fanwei Meng

“…Using an integral averaging method and generalized Riccati technique, by introducing a parameter β≥1, we derive new oscillation criteria for second-order partial differential equations with damping. The results are of high degree of generality and sharper than most known ones.…”
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Linear Hyperbolic Functional-Differential Equations with Essentially Bounded Right-Hand Side by Alexander Domoshnitsky, Alexander Lomtatidze, Abraham Maghakyan, Jiří Šremr

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Interaction between coefficient conditions and solution conditions of differential equations in the unit disk by K. E. Fowler, L. R. Sons

“…The influence of the normality of the coefficient A(z) of the differential equation f(k)+A(z)f=0 on a solution f and also the influence of the normality of a solution f on A(z) are investigated in the unit disk. …”
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On stability and boundedness of solutions of a certain fourth-order delay differential equation by Emmanuel O. Okoronkwo

“…Using a Razumikhin - type theorem, we deduce sufficient conditions that guarantee the uniform asymptotic stability and boundedness of solutions of a scalar real fourth-order delay differential equation. The Lyapunov function constructed for an ordinary fourth-order differential equation is seen to work for the delay system.…”
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On the Limit Cycles for a Class of Perturbed Fifth-Order Autonomous Differential Equations by Nabil Sellami, Romaissa Mellal, Bahri Belkacem Cherif, Sahar Ahmed Idris

“…We study the limit cycles of the fifth-order differential equation x⋅⋅⋅⋅⋅−ex⃜−dx⃛−cx¨−bx˙−ax=εFx,x˙,x¨,x⋯,x⃜ with a=λμδ,b=−λμ+λδ+μδ,c=λ+μ+δ+λμδ,d=−1+λμ+λδ+μδ,e=λ+μ+δ, where ε is a small enough real parameter, λ,μ, and δ are real parameters, and F∈C2 is a nonlinear function. …”
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Positive Solutions for System of Nonlinear Fractional Differential Equations in Two Dimensions with Delay by Azizollah Babakhani

“…We investigate the existence and uniqueness of positive solution for system of nonlinear fractional differential equations in two dimensions with delay. Our analysis relies on a nonlinear alternative of Leray-Schauder type and Krasnoselskii's fixed point theorem in a cone.…”
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Positive Solution of a Nonlinear Fractional Differential Equation Involving Caputo Derivative by Changyou Wang, Haiqiang Zhang, Shu Wang

“…This paper is concerned with a nonlinear fractional differential equation involving Caputo derivative. By constructing the upper and lower control functions of the nonlinear term without any monotone requirement and applying the method of upper and lower solutions and the Schauder fixed point theorem, the existence and uniqueness of positive solution for the initial value problem are investigated. …”
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Oscillation Criteria of First Order Neutral Delay Differential Equations with Variable Coefficients by Fatima N. Ahmed, Rokiah Rozita Ahmad, Ummul Khair Salma Din, Mohd Salmi Md Noorani

“…Some new oscillation criteria are given for first order neutral delay differential equations with variable coefficients. Our results generalize and extend some of the well-known results in the literature. …”
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Integral BVPs for a Class of First-Order Impulsive Functional Differential Equations by Xiaofei He, Jingli Xie, Guoping Chen, Jianhua Shen

“…International Journal of Differential Equations…”
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Laguerre Collocation Method for Solving Fredholm Integro-Differential Equations with Functional Arguments by Burcu Gürbüz, Mehmet Sezer, Coşkun Güler

“…Laguerre collocation method is applied for solving a class of the Fredholm integro-differential equations with functional arguments. This method transforms the considered problem to a matrix equation which corresponds to a system of linear algebraic equations. …”
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Asymptotically Almost Periodic Solutions for a Class of Stochastic Functional Differential Equations by Aimin Liu, Yongjian Liu, Qun Liu

“…This work is concerned with the quadratic-mean asymptotically almost periodic mild solutions for a class of stochastic functional differential equations dxt=Atxt+Ft,xt,xtdt+H(t,xt,xt)∘dW(t). …”
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Some Oscillation Results of Higher-Order Linear Differential Equations with Meromorphic Coefficients by Zhigang Huang

“…We investigate the growth of solutions of higher-order nonhomogeneous linear differential equations with meromorphic coefficients. We also discuss the relationship between small functions and solutions of such equations.…”
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A Novel Numerical Technique for Fractional Ordinary Differential Equations with Proportional Delay by Muhammad Imran Liaqat, Adnan Khan, Ali Akgül, Md. Shajib Ali

“…Some researchers have combined two powerful techniques to establish a new method for solving fractional-order differential equations. In this study, we used a new combined technique, known as the Elzaki residual power series method (ERPSM), to offer approximate and exact solutions for fractional multipantograph systems (FMPS) and pantograph differential equations (PDEs). …”
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Some Further Results on Oscillations for Neutral Delay Differential Equations with Variable Coefficients by Fatima N. Ahmed, Rokiah Rozita Ahmad, Ummul Khair Salma Din, Mohd Salmi Md Noorani

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Exponential stability for abstract linear autonomous functional differential equations with infinite delay by Jin Liang, Falun Huang, Tijun Xiao

Subjects: “…abstract linear autonomous functional differential equation…”
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On the Parametric Stokes Phenomenon for Solutions of Singularly Perturbed Linear Partial Differential Equations by Stéphane Malek

“…We study a family of singularly perturbed linear partial differential equations with irregular type in the complex domain. …”
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Existence Results for a Coupled System of Nonlinear Fourth-Order Differential Equations by Bessem Samet

“…Sufficient conditions are obtained for the existence of solutions to a coupled system of nonlinear fourth-order differential equations.…”
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A Novel Method for Solving Nonlinear Volterra Integro-Differential Equation Systems by Mohammad Hossein Daliri Birjandi, Jafar Saberi-Nadjafi, Asghar Ghorbani

“…An efficient iteration method is introduced and used for solving a type of system of nonlinear Volterra integro-differential equations. The scheme is based on a combination of the spectral collocation technique and the parametric iteration method. …”
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Existence of periodic solutions and homoclinic orbits for third-order nonlinear differential equations by O. Rabiei Motlagh, Z. Afsharnezhad

“…The existence of periodic solutions for the third-order differential equation x¨˙+ω2x˙=μF(x,x˙,x¨) is studied. We give some conditions for this equation in order to reduce it to a second-order nonlinear differential equation. …”
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Parameter Estimation in Ordinary Differential Equations Modeling via Particle Swarm Optimization by Devin Akman, Olcay Akman, Elsa Schaefer

“…Researchers using ordinary differential equations to model phenomena face two main challenges among others: implementing the appropriate model and optimizing the parameters of the selected model. …”
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