Yaremenko M.I.

Solvability of Quasi-Linear Elliptic Equation with Gilbar–Serrin Matrix in the Space Scale <em>R<sup>l</sup></em>

The study under scrutiny proves that it’s possible to solve the nonlinear differential equation in the second-order partial derivatives with operator coefficients in all Euclidean space Rl in the spaces scale W1p. We also propose a new class of operators associated with the given differential equation.

On solvability of the quasilinear elliptic equations with gilbarg-serrin matrix

The present paper articulates the second-order quasilinear elliptic equations with slow increasing coefficients in the whole Euclidean space Rl , l ≥ 3 . Furthermore, we deviate from the traditional point of view on the admissible class of the generalized solutions of the second-order elliptic equations, where the uniqueness theorem of Dirichlet problem is not exploited “in the small”. Instead, we prove the probability of the solution of the elliptic equations with Gilbarg-Serrin matrix.

On solvability of one classical linear elliptical differential second-order equation

The paper outlines the investigation of the linear elliptic equations on the whole Euclidean space Rl, l≥3. We obtain some results on the existence and uniqueness of the solutions of these equations.

On a single solvability of equation with matrix of Gilburg-Serin in sobol’s spaces

In this paper, we study the second-order quasilinear elliptic equations with slow-increasing coefficients on the Euclidean space Rl, l ≥ 3. We significantly broaden the concept of equation by introducing the weak coercitivity instead of the strong one. Our results show that this equation doesn’t satisfy the existence conditions of the solution “in the small”.

On solvability of the second-order quasilinear elliptic equations on the euclidean space R[sup]l[/sup], l[ge]3

The paper under consideration is devoted to investigation of the second-order quasi-linear elliptic equations with slowly increasing coefficients on the euclidean space Rl, l≥3.

On the smoothness of solutions of one quasilinear equation in R[sup]l[sup]

We consider the smoothness of solutions of quasilinear elliptic partial differential equations. In this paper we develop the form method for proving the conditions of Minty-Browder’s theorem, as well as for obtaining the research results on the smoothness of the solutions.

Second-order quaisi-linear elliptic equations with matrix of gilbarg–serrin and nonlinear semigroups of contraction. Part 1. On the solvability of the quasi-linear elliptic equations

The paper under consideration addresses the problem of studying the connection between elliptic equations with matrix of Gilbarg–Serrin and a generalized parabolic problem.