TY - GEN N1 - Bibliogr.: p. 17-20. ; összefoglalás angol nyelven UR - http://acta.bibl.u-szeged.hu/82283/ SN - 1417-3875 CY - Szeged AV - public ID - acta82283 TI - The Dirichlet problem in an unbounded cone-like domain for second order elliptic quasilinear equations with variable nonlinearity exponent EP - 20 Y1 - 2023/// KW - Elliptikus egyenlet KW - Laplace-egyenlet KW - Dirichlet probléma N2 - In this paper we consider the Dirichlet problem for quasi-linear second-order elliptic equation with the m(x)-Laplacian and the strong nonlinearity on the right side in an unbounded cone-like domain. We study the behavior of weak solutions to the problem at infinity and we find the sharp exponent of the solution decreasing rate. We show that the exponent is related to the least eigenvalue of the eigenvalue problem for the Laplace?Beltrami operator on the unit sphere. A1 - Borsuk Mikhail A1 - Wi?niewski Damian ER -