Álvarez Caudevilla, PabloEvans, J. D.Galaktionov, Victor A.2021-03-252021-03-252016-09-22Boundary Value Problems, (2016), Articel number: 171, (25) p.1687-2762https://hdl.handle.net/10016/32222Solutions 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.25eng© 2016 Álvarez-Caudevilla et al. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.Atribución-NoComercial-SinDerivadas 3.0 EspañaStationary Cahn-Hilliard equationVariational settingNon-Unique oscillatory solutionsCountable family of critical pointsresearch articleMatemáticashttps://doi.org/10.1186/s13661-016-0677-5open access117125Boundary Value Problems2016AR/0000018432