The Dirichlet problem in an unbounded cone-like domain for second order elliptic quasilinear equations with variable nonlinearity exponent

Autor: Mikhail Borsuk, Damian Wiśniewski
Jazyk: angličtina
Rok vydání: 2023
Předmět:
Zdroj: Electronic Journal of Qualitative Theory of Differential Equations, Vol 2023, Iss 33, Pp 1-20 (2023)
Druh dokumentu: article
ISSN: 1417-3875
DOI: 10.14232/ejqtde.2023.1.33
Popis: 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.
Databáze: Directory of Open Access Journals