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Boundary Value Problems for the q — Laplacian on 𝕊 N
Author(s) -
Bandle C.,
Fleckinger J.,
de Thélin F.
Publication year - 2001
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 - 10.1002/1522-2616(200104)224:1<5::aid-mana5>3.0.co;2-m
Subject(s) - mathematics , laplace operator , euclidean space , nonlinear system , curvature , boundary value problem , mathematical analysis , space (punctuation) , constant (computer programming) , boundary (topology) , euclidean geometry , pure mathematics , calculus (dental) , geometry , medicine , linguistics , philosophy , physics , dentistry , quantum mechanics , computer science , programming language
Nonlinear boundary value problems for the q –Laplacian in spaces of constant positive curvature are considered. The nonlinearity is of the form of a power. Existence and nonexistence of positive radial solutions in balls is established. It turns out that the situation differs considerably from the corresponding problems in the Euclidean space. Special attention is given to the critical case which has some consequences in the calculus of variation.