Multiplicity of layered solutions for Allen-Cahn systems with symmetric double well potential

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:257

Article

Alessio, Francesca¹  Montecchiari, Piero¹ 

[1] Univ Politecn Marche, Dipartimento Ingn Ind & Sci Matemat, I-60131 Ancona, Italy

关键词: Entire solutions;    Semi linear elliptic systems;    Variational methods;   

DOI  :  10.1016/j.jde.2014.09.001

来源: Elsevier

【 摘 要 】

We study the existence of solutions u : R-3 -> R-2 for the semilinear elliptic systems -Delta u(x,y,Z) + Delta W(u(x, y, z)) = 0, (0.1) where W : R-2 -> R is a double well symmetric potential. We use variational methods to show, under generic non-degenerate properties of the set of one dimensional heteroclinic connections between the two minima a +/- of W, that (0.1) has infinitely many geometrically distinct solutions u is an element of C-2(R-3, R-2) which satisfy u (x, y, z) -> a +/- as x -> +/-infinity uniformly with respect to (y, z) is an element of R-2 and which exhibit dihedral symmetries with respect to the variables y and z. We also characterize the asymptotic behavior of these solutions as vertical bar(y,z)vertical bar -> +infinity. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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