We consider a class of semilinear elliptic system of the form −∆u(x,y)+∇W(u(x,y))=0, (x,y)∈R2, where W : R2 → R is a double well non negative symmetric potential. We show, via variational methods, that if the set of solutions to the one dimensional system −q ̈(x) + ∇W(q(x)) = 0, x ∈ R, which connect the two minima of W as x → ±∞ has a discrete structure, then the system has infinitely many layered solutions.
Stationary layered solutions for a system of Allen-Cahn type equations / Alessio, FRANCESCA GEMMA. - In: INDIANA UNIVERSITY MATHEMATICS JOURNAL. - ISSN 0022-2518. - STAMPA. - 62:5(2013), pp. 1535-1564. [10.1512/iumj.2013.62.5108]
Stationary layered solutions for a system of Allen-Cahn type equations
ALESSIO, FRANCESCA GEMMA
2013-01-01
Abstract
We consider a class of semilinear elliptic system of the form −∆u(x,y)+∇W(u(x,y))=0, (x,y)∈R2, where W : R2 → R is a double well non negative symmetric potential. We show, via variational methods, that if the set of solutions to the one dimensional system −q ̈(x) + ∇W(q(x)) = 0, x ∈ R, which connect the two minima of W as x → ±∞ has a discrete structure, then the system has infinitely many layered solutions.File in questo prodotto:
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