RT Journal Article
T1 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
A1 Álvarez Caudevilla, Pablo
A1 Evans, J. D.
A1 Galaktionov, Victor A.
AB Solutions of the stationary semilinear Cahn-Hilliard-type equation (...) which are exponentially decaying at infinity, are studied. Using the mounting passlemma allows us to determinate the existence of a radially symmetric solution. On theother hand, the application of Lusternik-Schnirel’man (L-S) category theory shows theexistence 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 beobtained by the L-S min-max approach.
PB SpringerOpen
SN 1687-2762
YR 2016
FD 2016-09-22
LK https://hdl.handle.net/10016/32222
UL https://hdl.handle.net/10016/32222
LA eng
NO The authors would like to thank the anonymous referees by their valuable suggestions, helpful comments which further improved the content and presentation of the paper. Also, this work has been partially supported by the Ministry of Economy and Competitiveness of Spain under research project MTM2012-33258. The first author has also been supported by the Ramón y Cajal project RYC-2014-15284 of the Ministry of Economy and Competitiveness.
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RD 27 jul. 2024