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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]

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