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Article Dans Une Revue Nonlinear Differential Equations and Applications Année : 2016

Layered solutions for a fractional inhomogeneous Allen–Cahn equation

Résumé

We consider the problem e(2s) (-partial derivative(xx))(s)u(x) - V (x) over bar (u)over bar(x)over bar (1-u(2))((x)over bar) = 0 where (-partial derivative xx)(s) denotes the usual fractional Laplace operator, epsilon > 0 is a small parameter and the smooth bounded function V satisfies infi x is an element of R V (x) > 0. For a E 1), we prove the existence of separate multi layered solutions for any small a, where the layers are located near any non -degenerate local maximal points and non-degenerate local minimal points of function V. We also prove the existence of clustering-layered solutions, and these clustering layers appear within a very small neighborhood of a local maximum point of V.

Dates et versions

hal-01486976 , version 1 (09-10-2023)

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Citer

Zhuoran Du, Changfeng Gui, Yannick Sire, Juncheng Wei. Layered solutions for a fractional inhomogeneous Allen–Cahn equation. Nonlinear Differential Equations and Applications, 2016, 23 (3), ⟨10.1007/s00030-016-0384-z⟩. ⟨hal-01486976⟩
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