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