Multiple Periodic Solutions of a Class of Fractional Laplacian Equations
Copyright policy )Multiple Periodic Solutions of a Class of Fractional Laplacian Equations
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.
- Utah State University United States
- Tianjin University China (People's Republic of)
- Tianjin University China (People's Republic of)
- Fujian Normal University China (People's Republic of)
35b10, fractional laplacian, periodic solution, Nonlinear elliptic equations, 35a15, 35j60, Morse index, morse index, Variational methods applied to PDEs, minimax method, QA1-939, fractional Laplacian, Mathematics, Periodic solutions to PDEs
35b10, fractional laplacian, periodic solution, Nonlinear elliptic equations, 35a15, 35j60, Morse index, morse index, Variational methods applied to PDEs, minimax method, QA1-939, fractional Laplacian, Mathematics, Periodic solutions to PDEs
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