References
- Caffarelli L, Silvestre L. An extension problem related to the fractional Laplacian. Commun Partial Differ Equ. 2007;32:1245–1260. doi: 10.1080/03605300600987306
- Di Nezza E, Palatucci G, Valdinoci E. Hitchhikers guide to the fractional Sobolev spaces. Bull Sci Math. 2012;136:521–573. doi: 10.1016/j.bulsci.2011.12.004
- Wang J, Du Z. Multiple entire solutions of fractional Laplacian Schrödinger equation. J AIMS Math. 2021;6:8509–8524. doi: 10.3934/math.2021494
- Gui C, Zhang J, Du Z. Periodic solutions of a semilinear elliptic equation with a fractional Laplacian. J Fixed Point Theory Appl. 2017;19:363–373. doi: 10.1007/s11784-016-0357-1
- Du Z, Gui C. Further study on periodic solutions of elliptic equations with a fractional Laplacian. Nonlinear Anal. 2020;193:111417. doi: 10.1016/j.na.2019.01.007
- Feng Z, Du Z. Periodic solutions of fractional Laplace equations: least period, axial symmetry and limit. 2022;60:633–651.
- Feng Z, Du Z. Periodic solutions of non-autonomous Allen-Cahn equations involving fractional Laplacian. Adv Nonlinear Stud. 2020;20:725–737. doi: 10.1515/ans-2020-2075
- Cui Y, Wang Z. Multiple periodic solutions of a class of fractional Laplacian equations. Adv Nonlinear Stud. 2020;21:41–56. doi: 10.1515/ans-2020-2113
- Du Z, Gui C. Periodic solutions of Allen-Cahn system with the fractional Laplacian. Nonlinear Anal. 2020;201:112061. doi: 10.1016/j.na.2020.112061
- Barrios B, Garcría -Melián J, Quass A. Periodic solutions for the one-dimensional fractional Laplacian. J Differ Equ. 2019;267:5258–5289. doi: 10.1016/j.jde.2019.05.031
- Ambrosio V. Infinitely many periodic solutions for a fractional problem under perturbation. J Elliptic Parabol Equ. 2016;2:105–117. doi: 10.1007/BF03377395
- Ambrosio V. On the existence of periodic solutions for a fractional Schrödinger equation. Proc Amer Math Soc. 2018;146:3767–3775. doi: 10.1090/proc/2018-146-09
- Ambrosio V. Periodic solutions for critical fractional problems. Calc Var Partial Differ Equ. 2018;57:1–31. doi: 10.1007/s00526-017-1276-8Paper No. 45.
- DelaTorre A, del Pino M, González M, et al. Delaunay-type singular solutions for the fractional Yamabe problem. Math Ann. 2017;369:597–626. doi: 10.1007/s00208-016-1483-1
- DelaTorre A, del Mar González M. Isolated singularities for a semilinear equation for the fractional Laplacian arising in conformal geometry. Rev Math Iberoam. 2018;34:1645–1678. doi: 10.4171/RMI
- Kryszewski W, Szulkin A. Generalized linking theorem with application semilinear Schrödinger equation. Adv Differ Equ. 1998;3:441–472.
- Li G, Szulkin A. An asymptotically periodic Schrödinger equation with indefinite linear part. Commun Contemp Math. 2002;4:763–776. doi: 10.1142/S0219199702000853
- Birman M, Solomjak M. Spectral theory of Self-Adjoint operators in Hilbert space. Dordrecht, Boston, Lancaster, Tokyo: D. Reidel Publishing Company; 1986.
- Edmunds D, Evans W. Spectral theory and differential operators. Oxford: Clarendon Press; 1987.
- Fang F, Ji C. On a fractional Schrödinger equation with periodic potential. Comput Math Appl. 2019;78:1517–1530. doi: 10.1016/j.camwa.2019.03.044