We find conditions under which all solutions of stochastic algebraic-differential equations given in terms of forward Nelson’s mean derivatives, exist for all t ∈ [0, ∞). We suppose that the matrix pencil of equation satisfies the rank-degree condition.

In paper we investigate solvability of the variational Dirichlet problem for a class of elliptic differential operators in the whole space. The sesquilinear form associated with the operator under study is represented as a finite sum of auxiliary sesquilinear forms and the concept of “leading form” is introduced. Depending on the behavior of the coefficients of the leading forms, the main weighted space of differentiable functions of many real variables in the entire space is introduced. The solvability of the variational Dirichlet problem is studied in this space.

The paper presents a mathematical model of a stationary wave of filtration combustion of gases, taking into account heat transfer to the surrounding space and diffusion coefficients of the components of the mixture of gases.

This study presents precise batch solutions for electrical circuit systems using Jacobi elliptical functions snξ, cnξ, and dnξ.