Existence of heteroclinic solutions for a class of problems involving the fractional Laplacian.

In this paper, we study the existence of heteroclinic solution for a class of nonlocal problems of the type (− Δ) α u + a (𝜖 x) V ′ (u) = 0 , x ∈ ℝ , lim x → − ∞ u (x) = − 1 and lim x → + ∞ u (x) = 1 , where α ∈ (1 / 2 , 1) , V , a : ℝ → ℝ are continuous functions verifying some technical conditions. For example a can be asymptotically periodic and potential V can be the Ginzburg–Landau potential, that is, V (t) = (t 2 − 1) 2 . [ABSTRACT FROM AUTHOR]