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On the Existence of Radial Solutions of a Nonlinear Elliptic BVP in an Annulus
Author(s) -
Cheng Yuanji
Publication year - 1994
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19941650106
Subject(s) - mathematics , annulus (botany) , nonlinear system , mathematical analysis , elliptic curve , boundary value problem , pure mathematics , physics , botany , quantum mechanics , biology
In this paper we study the radial solutions of quasilinear elliptic BVP:\documentclass{article}\pagestyle{empty}\begin{document}$ div (a(|x|,\,u,|\nabla u|)\nabla u) + f(|x|,\,u,\,|\nabla u|) = 0 $\end{document} on A , u satisfies the Robin boundary conditions (2) below, where A = { x ∈ R n ; a 1 < | x | < a 2 }, a 2 > a 1 > 0, constants. Under the very general conditions, we prove that if f is superlinear at u = ∞, then (*) admits infinitely many radial solutions, and that each of them has a different (finite) number of zeros.