Publication: Countable Families of solutions of a limit sationay semilinear fourth-order cahn-hillard-type equation I. Mountain pass and Lusternik-Schirel'man patterns in R^N
Loading...
Identifiers
Publication date
2016-09-22
Defense date
Advisors
Tutors
Journal Title
Journal ISSN
Volume Title
Publisher
SpringerOpen
Abstract
Solutions of the stationary semilinear Cahn-Hilliard-type equation (...)
which are exponentially decaying at infinity, are studied. Using the mounting pass
lemma allows us to determinate the existence of a radially symmetric solution. On the
other hand, the application of Lusternik-Schnirel’man (L-S) category theory shows the
existence of, at least, a countable family of solutions.
However, through numerical methods it is shown that the whole set of solutions,
even in 1D, is much wider. This suggests that, actually, there exists, at least,
a countable set of countable families of solutions, in which only the first one can be
obtained by the L-S min-max approach.
Description
Keywords
Stationary Cahn-Hilliard equation, Variational setting, Non-Unique oscillatory solutions, Countable family of critical points
Bibliographic citation
Boundary Value Problems, (2016), Articel number: 171, (25) p.