This paper is devoted to local static bifurcation theory for a class of degenerate boundary value problems for nonlinear second-order elliptic differential operators. The purpose of this paper is twofold. The first purpose is to prove that the first eigenvalue of the linearized boundary value problem is simple and its associated eigenfunction is positive. The second purpose is to discuss the changes that occur in the structure of the solutions as a parameter varies near the first eigenvalue of the linearized problem.
@article{urn:eudml:doc:40350,
title = {Bifurcation for nonlinear elliptic boundary value problems I.},
journal = {Collectanea Mathematica},
volume = {47},
year = {1996},
pages = {207-229},
zbl = {0865.35014},
mrnumber = {MR1437653},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40350}
}
Taira, Kazuaki. Bifurcation for nonlinear elliptic boundary value problems I.. Collectanea Mathematica, Tome 47 (1996) pp. 207-229. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40350/