Periodic Solutions of Non-autonomous Allen–Cahn Equations Involving Fractional Laplacian

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Periodic Solutions of Non-autonomous Allen–Cahn Equations Involving Fractional Laplacian

Feng, Zhenping; Du, Zhuoran

Advanced nonlinear studies, 08/2020, Volume: 20, Issue: 3

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We consider periodic solutions of the following problem associated with the fractional Laplacian: in . The smooth function is periodic about and is a double-well potential with respect to with wells at and -1 for any . We prove the existence of periodic solutions whose periods are large integer multiples of the period of about the variable by using variational methods. An estimate of the energy functional, Hamiltonian identity and Modica-type inequality for periodic solutions are also established.

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