Abstract
Abstract In this paper, we study the existence of multiple periodic solutions for the following fractional equation: ( - Δ ) s u + F ′ ( u ) = 0 , u ( x ) = u ( x + T ) x ∈ ℝ . (-\Delta)^{s}u+F^{\prime}(u)=0,\qquad u(x)=u(x+T)\quad x\in\mathbb{R}. For an even double-well potential, we establish more and more periodic solutions for a large period T. Without the evenness of F we give the existence of two periodic solutions of the problem. We make use of variational arguments, in particular Clark’s theorem and Morse theory.
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