MMN-1290
Bifurcation Problems for Noncompact Operators
Abstract
Under new hypotheses, and using the Lyapunov-Schmidt reduction, we study the
branches of bifurcation of a nonlinear equation of the type $u - \lambda Lu + G(\lambda, u) = 0$, in a
neighborhood $W$ of a particular solution $(\lambda_0, 0)\in \mathbb{R}\times X$, where $X$ is a real Banach space, $L$ a non-compact linear
operator defines on $X$ and $G$ is a nonlinear operator defined on $W$ to values in
$X$. This type of bifurcation problems ( bifurcation
from the trivial branch ) have different applications such as resolution of differential
equations as those of Von-Karmann and Navier-Stokes or to integral equations as the Urysohn's one.
Vol. 17 (2016), No. 1, pp. 571-580
DOI: 10.18514/MMN.2016.1290