Affiliation:
1. Dipartimento di Scienze Matematiche, Università Politecnica delle Marche, via Brecce Bianche, I-60131 Ancona
Abstract
Abstract
We consider a class of semilinear elliptic equations of the form
−Δu(x,y) + a(εx)Wʹ(u(x,y)) = 0, (x,y) ∊ ℝ2 (0.1)
where ε > 0, a : ℝ → ℝ is an almost periodic, positive function and W : ℝ → ℝ is modeled on the classical two well Ginzburg-Landau potential W(s) = (s2 - 1)2. We show via variational methods that if ε is sufficiently small and a is not constant then (0.1) admits infinitely many two dimensional entire solutions verifying the asymptotic conditions u(x, y) → ±1 as x → ±∞ uniformly with respect to y ∊ ℝ.
Subject
General Mathematics,Statistical and Nonlinear Physics
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