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In this paper the asymptotic distributions are exactly solved for linearly independent solutions considering problems of the second order and for the coefficients of asymptotic destribution the recurent formulas are obtained. Further, using…
We explore the limit of stochastic differential equations driven by some random processes satisfying singularly perturbed second order stochastic differential equations. The main tool we employ is the universal limit theorem in rough path…
The paper conducts a second-order variational analysis for an important class of nonpolyhedral conic programs generated by the so-called second-order/Lorentz/ice-cream cone $Q$. From one hand, we prove that the indicator function of $Q$ is…
We identify many new solvable subcases of the general dynamical system characterized by two autonomous first-order ordinary differential equations with purely quadratic right-hand sides; the solvable character of these dynamical systems…
A novel fourth-order finite difference formula coupling the Crank-Nicolson explicit linearized method is proposed to solve Riesz space fractional nonlinear reaction-diffusion equations in two dimensions. Theoretically, under the Lipschitz…
We solve some forms of non homogeneous differential equations in one and two dimensions. By expanding the solution into whell-posed closed form-Eisenstein series the solution itself is quite simple and elementary. Also we consider Fourier…
Let $L$ be a second-order elliptic operator with analytic coefficients defined in $B_1\subseteq\mathbb R^n$. We construct explicitly and canonically a fundamental solution for the operator, i.e., a function $u:B_{r_0}\to\mathbb R$ such that…
The averaging theory has been extensively employed for studying periodic solutions of smooth and nonsmooth differential systems. Here, we extend the averaging theory for studying periodic solutions a class of regularly perturbed…
In this paper, we develop the averaging principle for a class of two-time-scale stochastic reaction-diffusion equations driven by Wiener processes and Poisson random measures. We assume that all coefficients of the equation have polynomial…
We consider wave equations on Lorentzian manifolds in case of low regularity. We first extend the classical solution theory to prove global unique solvability of the Cauchy problem for distributional data and right hand side on smooth…
This paper studies the existence and global stability of generalized Ornstein-Uhlenbeck process for affine stochastic functional differential equations. Various very basic and important properties are established. In the applications, we…
In this paper, we propose second-order sufficient optimality conditions for a very general nonconvex constrained optimization problem, which covers many prominent mathematical programs.Unlike the existing results in the literature, our…
The problem of fitting experimental data to a given model function $f(t; p_1,p_2,\dots,p_N)$ is conventionally solved numerically by methods such as that of Levenberg-Marquardt, which are based on approximating the Chi-squared measure of…
Basing on Picard-Vessiot theory of noncommutative differential equations and algebraic combinatorics on noncommutative formal series with holomorphic coefficients, various recursive constructions of sequences of grouplike series converging…
The aim of this work is to prove existence and uniqueness results for a doubly nonlinear elliptic problem that is essential for solving the associated parabolic problem using Rothe's method (discretizing time). We work under very weak…
It is well known that second order linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation is the basis of the Liouville-Green method and many other techniques for the…
We propose a second order differential calculus to analyze the regularity and the stability properties of the distribution semigroup associated with McKean-Vlasov diffusions. This methodology provides second order Taylor type expansions…
In traditional work on numerical schemes for solving stochastic differential equations (SDEs), it is usually assumed that the coefficients are globally Lipschitz. This assumption has been used to establish a powerful analysis of the…
We provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range amongst those with unbalanced…
The results of this study are continuation of the research of Poincar\'e chaos initiated in papers (Akhmet M, Fen MO. Commun Nonlinear Sci Numer Simulat 2016;40:1-5; Akhmet M, Fen MO. Turk J Math, doi:10.3906/mat-1603-51, accepted). We…