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In this paper, we study the second-order quasilinear elliptic equations with slow-increasing coefficients on the Euclidean space R¹ , , 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". [ABSTRACT FROM AUTHOR]

The paper outlines the investigation of the linear elliptic equations on the whole Euclidean space R¹ ,l ⩾ 3 . We obtain some results on the existence and uniqueness of the solutions of these equations. [ABSTRACT FROM AUTHOR]

The paper under consideration is devoted to investigation of the second-order quasi-linear elliptic equations with slowly increasing coefficients on the euclidean space R¹, l ≥ 3. [ABSTRACT FROM AUTHOR]

This paper deals with the connection between elliptic equations with Gilbarg-Serrin matrix and the generalized parabolic problems. [ABSTRACT FROM AUTHOR]

The paper under consideration addresses the problem of studying the connection between elliptic equations with matrix of Gilbarg-Serrin and a generalized parabolic problem. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The work is devoted to investigation of the second-order quaisi-linear elliptic equations with slow-increasing coefficients on the Euclidean space R l , l ? 3. There, authors reject a traditional point of view at the admissible class of generalized solutions of the second-order elliptic equations in which the uniqueness theorem for Dirichlet problem "in the small" is not held. [ABSTRACT FROM AUTHOR]

The work is devoted to investigation of the second-order quasi-linear elliptic equations with slow-increasing coefficients on the Euclidean space R¹, 1 ≥ 3. The authors reject a traditional point of view at the admissible class of generalized solutions of the second-order elliptic equations in which the uniqueness theorem for Dirichlet problem "in the small" is not held. In the next part of the paper a nonlinear analogue of the Hille-Josida-Phillips theorem is proved in Lp(R¹,d¹x). [ABSTRACT FROM AUTHOR]

The equation was considered in numerous works of well-known mathematicians, as an example for which the uniqueness theorem for the Dirichlet problem ‘in the small’ is not held. The equation global solvability in R1 was established, proven theorem-analogue of the Minti-Brauder theorem was proved. [ABSTRACT FROM AUTHOR]

The work is the logical continuation of the works by N.M. Kukharchuk ‘On solvability of the high-order quasi-linear elliptic equations in Rℓ’, ‘Dissipative operators and nonlinear semigroups of compressions in Lp(Rℓ,dℓ x)’. It was established, that the operators, which are generated by the form, that was explored in the first of the afore-mentioned works, are generators of nonlinear semigroups of compressions in L²(Rℓ , dℓ d x , i.e. nonlinear analogue of the theorem of Hille-losida-Fillips is proved in L²(Rℓ ,dℓx) analysed. [ABSTRACT FROM AUTHOR]