Article Contents
Article Contents

# Layer solutions for an Allen-Cahn type system driven by the fractional Laplacian

• We study entire solutions in $R$ of the nonlocal system $(-\Delta)^{s}U+\nabla W(U)=(0,0)$ where $W:R^{2}\rightarrow R$ is a double well potential. We seek solutions $U$ which are heteroclinic in the sense that they connect at infinity a pair of global minima of $W$ and are also global minimizers. Under some symmetric assumptions on potential $W$, we prove the existence of such solutions for $s>\frac{1}{2}$, and give asymptotic behavior as $x\rightarrow\pm\infty$.
Mathematics Subject Classification: 82B26, 49Q20, 26A33, 49J45.

 Citation:

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