Limit-Point/Limit-Circle Results for Equations with Damping by M. Bartušek, John R. Graef

“…The authors study the nonlinear limit-point and limit-circle properties for the second order nonlinear damped differential equation (a(t)|y'|p-1y')'+b(t)|y'|q-1y'+r(t)|y|λ-1y=0, where 0<λ≤p≤q, a(t)>0, and r(t)>0. …”
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Solutions and Conservation Laws of a (2+1)-Dimensional Boussinesq Equation by Letlhogonolo Daddy Moleleki, Chaudry Masood Khalique

“…We study a nonlinear evolution partial differential equation, namely, the (2+1)-dimensional Boussinesq equation. …”
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Pricing Parisian Option under a Stochastic Volatility Model by Min-Ku Lee, Kyu-Hwan Jang

“…A stochastic volatility correction to the Black-Scholes price of the Parisian option is obtained in a partial differential equation form and the solution is characterized numerically.…”
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Controllability in Hybrid Kinetic Equations Modeling Nonequilibrium Multicellular Systems by Carlo Bianca

“…Specifically, the analysis shows that the moments are solution of a Riccati-type differential equation.…”
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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.…”
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On nth-order differential operators with Bohr-Neugebauer type property by Aribindi Satyanarayan Rao

“…If the differential operator dndtn−B has a Bohr-Neugebauer type property for Bochner almost periodic functions, then, for any Stepanov almost periodic continuous function g(t) and any Stepanov-bounded solution of the differential equation dndtnu(t)−Bu(t)=g(t), u(n−1),…,u′,u are all almost periodic.…”
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A Numerical Method for Computing the Principal Square Root of a Matrix by F. Soleymani, S. Shateyi, F. Khaksar Haghani

“…Finally, application of the presented approach is illustrated in solving a matrix differential equation.…”
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Machine learning to identify environmental drivers of phytoplankton blooms in the Southern Baltic Sea by Maximilian Berthold, Pascal Nieters, Rahel Vortmeyer-Kley

“…We employed generalized additive mixed models to characterize similar blooming patterns and trained an artificial neural network within the Universal Differential Equation framework to learn a differential equation representation of these pattern. …”
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The Pricing of Vulnerable Options in a Fractional Brownian Motion Environment by Chao Wang, Shengwu Zhou, Jingyuan Yang

“…Under the assumption of the stock price, interest rate, and default intensity obeying the stochastic differential equation driven by fractional Brownian motion, the jump-diffusion model is established for the financial market in fractional Brownian motion setting. …”
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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.…”
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On a Fractional SPDE Driven by Fractional Noise and a Pure Jump Lévy Noise in ℝd by Xichao Sun, Zhi Wang, Jing Cui

“…We study a stochastic partial differential equation in the whole space x∈ℝd, with arbitrary dimension d≥1, driven by fractional noise and a pure jump Lévy space-time white noise. …”
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Nematic Liquid Crystal Locking Menisci by Milan Svetec, Mitja Slavinec

“…The resulting Euler-Lagrange differential equation is solved numerically. We determine conditions for the defects to be trapped by the meniscus.…”
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Permanence, Extinction, and Almost Periodic Solution of a Nicholson's Blowflies Model with Feedback Control and Time Delay by Haihui Wu, Shengbin Yu

“…By applying the comparison theorem of the differential equation and fluctuation lemma and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence, extinction, and existence of a unique globally attractive positive almost periodic solution of the system are obtained. …”
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Study of Time Evolution for Approximation of Two-Body Spinless Salpeter Equation in Presence of Time-Dependent Interaction by Hadi Sobhani, Hassan Hassanabadi

“…We use the Lewis-Riesenfeld dynamical invariant method and series solution to obtain the solutions of the differential equation. We have also done some calculations in order to derive the time evolution operator for the considered problem.…”
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A relationship between the modified Euler method and e by Richard B. Darst, Thomas P. Dence

“…Approximating solutions to the differential equation dy/dx=f(x,y) where f(x,y)=y by a generalization of the modified Euler method yields a sequence of approximates that converge to e. …”
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New Applications of a Kind of Infinitesimal-Operator Lie Algebra by Honwah Tam, Yufeng Zhang, Xiangzhi Zhang

“…Applying some reduced Lie algebras of Lie symmetry operators of a Lie transformation group, we obtain an invariant of a second-order differential equation which can be generated by a Euler-Lagrange formulism. …”
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Further studies of fully developed flow through ducts of arbitrary section by the contour line-conformal mapping technique by J. Mazumdar, D. Hopkins

“…The amplitude of the oscillatory velocity is then obtained from an ordinary integro-differential equation. Several examples of a practical nature are given, with some that have not yet been discussed in the literature. …”
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An Efficient Method for Solving Spread Option Pricing Problem: Numerical Analysis and Computing by R. Company, V. N. Egorova, L. Jódar

“…This paper deals with numerical analysis and computing of spread option pricing problem described by a two-spatial variables partial differential equation. Both European and American cases are treated. …”
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On the spectrum of a stationary problem with nonlocal integral type boundary condition by Sigita Pečiulytė, Olga Štikonienė, Artūras Štikonas

“… We investigated a eigenvalue problem for simple second order ordinary differential equation with one inte­gral type nonlocal boundary condition. …”
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Approximate Solutions of Delay Parabolic Equations with the Dirichlet Condition by Deniz Agirseven

“…Finite difference and homotopy analysis methods are used for the approximate solution of the initial-boundary value problem for the delay parabolic partial differential equation with the Dirichlet condition. The convergence estimates for the solution of first and second orders of difference schemes in Hölder norms are obtained. …”
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