The fibering method applied to the level sets of a family of functionals.

Abstract:  Given an one-parameter family of C1-functionals, Φμ : X →R, defined on an uniformly convex Banach space X, we describe a method
that permit us find critical points of Φμ at some energy level c ∈ R.
In fact, we show the existence of a sequence μ(n,c), n ∈N, such that
Φμ(n,c) has a critical level at c ∈ R, for all n ∈ N. Moreover, we
show some good properties of the curves μ(n,c), with respect to c (for
example, they are Lipschitz), and as a consequence of this analysis,
we recover many know results on the literature concerning bifurca-
tions of elliptic partial differential equations. Furthermore we prove
new results for a large class of elliptic partial differential equations,
which includes, for example, Ouyang, Lane-Enden, Concave-Convex,
Kirchhoff and Schr ̈odinger-Bopp-Podolsky type equations.

Date: Dec 16, 2021 at 16:15:00 h
Venue: Modalidad Vía Online.
Speaker: Kaye Silva
Affiliation: Universidade Federal de Goiás, Brazil
Coordinator: Gabrielle Nornberg
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Posted on Dec 10, 2021 in Differential Equations, Seminars