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Existence of positive radial solutions for a nonlinear elliptic problem in annulus domains
Author(s) -
Deng Jian
Publication year - 2012
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2547
Subject(s) - annulus (botany) , mathematics , domain (mathematical analysis) , degenerate energy levels , mathematical analysis , nonlinear system , star (game theory) , elliptic curve , physics , botany , quantum mechanics , biology
In this paper, we study a nonlinear elliptic problem in an annulus domain. For which, the nonexistence of nontrivial solutions has been obtained by some authors in star‐shaped domain. Although we note that it may admit non‐trivial solutions if the domain is non‐star shaped. With the use of a variational method, we establish the existence of positive radial solutions in an annulus domain. On the basis of this, we also extend this result to the periodic problem of the corresponding degenerate parabolic problem. Copyright © 2012 John Wiley & Sons, Ltd.