Bifurcation at isolated singular points for a degenerate elliptic eigenvalue problem

We consider bifurcation from the line of trivial solutions for a nonlinear eigenvalue problem on a bounded open subset, Omega, of R-N with N >= 3, containing 0. The leading term is a degenerate elliptic operator of the form L(u) = del . A del u where A is an element of C((Omega) over bar) with A > 0 on (Omega) over bar {0} and lim(x -> 0) A(x)/vertical bar x vertical bar(2) is an element of (0, infinity). Solutions should satisfy u = 0 on partial derivative Omega and the energy associated with L should be finite: integral(Omega) A vertical bar del u vertical bar(2)dx < infinity. The nonlinear terms are of lower order, depending only on u and del u. Under our hypotheses the associated Nemytskii operators are not Frechet differentiable at the trivial solution u = 0. (C) 2014 Elsevier Ltd. All rights reserved.


Published in:
Nonlinear Analysis-Theory Methods & Applications, 119, 209-221
Year:
2015
Publisher:
Oxford, Pergamon-Elsevier Science Ltd
ISSN:
0362-546X
Keywords:
Laboratories:




 Record created 2015-05-29, last modified 2018-09-13


Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)