On the decay at infinity of solutions of fractional Schrödinger equations

References

• Meshkov VZ. On the possible rate of decay at infinity of solutions of second order partial differential equations. Math USSR-Sb. 1992;72(2):343–361. doi: 10.1070/SM1992v072n02ABEH001414
   Google Scholar
• Astakhov AT, Meshkov VZ. On the possible decay at infinity of solutions of homogeneous elliptic equations. Differ Equ. 2014;50(11):1548–1550. doi: 10.1134/S0012266114110123
   Web of Science ®Google Scholar
• Sampedro JC. Unique continuation at infinity of solutions to Schrödinger equations with complex-valued potentials. Proc Edinburgh Math Soc. 1999;42:143–153. doi: 10.1017/S0013091500020071
   Web of Science ®Google Scholar
• El Aïdi M. On a unique continuation for Aharonov Bohm magnetic Schrödinger equation. Forum Math. 2017;29(6):1349–1354. doi: 10.1515/forum-2016-0161
   Web of Science ®Google Scholar
• Caffarelli L, Silvestre L. An extension problem related to the fractional Laplacian. Comm Partial Differ Equ. 2007;32(7–9):1245–1260. doi: 10.1080/03605300600987306
   Web of Science ®Google Scholar
• Bucur C, Valdinoci E. Nonlocal diffusion and applications. Lecture Notes of the Unione Matematica Italiana 20. Springer, [Cham]; Unione Matematica Italiana, Bologna, 2016 xii+155 pp.
   Google Scholar
• Friedman A. PDE problems arising in mathematical biology. Netw Heterog Media. 2012;7(4):691–703. doi: 10.3934/nhm.2012.7.691
   Web of Science ®Google Scholar
• Humphries NE, Queiroz N, Dyer JR, et al. Environmental context explains Lévy and Brownian movement patterns of marine predators. Nature. 2010;465(7301):1066–1069. doi: 10.1038/nature09116
   PubMed Web of Science ®Google Scholar
• Reynolds A, Rhodes C. The Lévy flight paradigm: random search patterns and mechanisms. Ecology. 2009;90(4):877–887. doi: 10.1890/08-0153.1
   PubMed Web of Science ®Google Scholar
• Schoutens W. Lévy processes in finance: pricing financial derivatives. New York: John Wiley and Sons, Ltd; 2003. Wiley Series in Probability and Statistics.
   Google Scholar
• Viswanathan GM, Afanasyev V, Buldyrev SV, et al. Lévy flight search patterns of wandering albatrosses. Nature. 1996;381(6581):413–415. doi: 10.1038/381413a0
   Web of Science ®Google Scholar
• Woyczyński WA. Levy processes in the physical sciences. In Lévy processes, pages 241–266. Birkhäuser Boston, Boston, MA, 2001.
   Google Scholar
• Rüland A. Unique continuation for fractional Schrödinger equations with rough potentials. Commun Partial Differ Equ. 2015;40(1):77–114. doi: 10.1080/03605302.2014.905594
   Web of Science ®Google Scholar
• Frank RL, Lenzmann E. Uniqueness of non-linear ground states for fractional Laplacians in R. Acta Math. 2013;210:261–318. doi: 10.1007/s11511-013-0095-9
   Web of Science ®Google Scholar
• Frank RL, Lenzmann E, Silvestre L. Uniqueness of radial solutions for the fractional Laplacian. Comm Pure Appl Math. 2016;69(99):1671–172. doi: 10.1002/cpa.21591
   Google Scholar
• Chen W, Li C, Ou B. Classification of solutions for an integral equation. Comm Pure Appl Math. 2006;59:330–343. doi: 10.1002/cpa.20116
   Web of Science ®Google Scholar
• Carmona R, Masters WC, Simon B. Relativistic Schrödinger operators: asymptotic behavior of the eigenfunctions. J Funct Anal. 1990;91:117–142. doi: 10.1016/0022-1236(90)90049-Q
   Web of Science ®Google Scholar
• Abatangelo N, Valdinoci E. Getting acquainted with the fractional Laplacian, to appear on Springer-INdAM Series, INdAM Intensive Period “Contemporary Research in elliptic PDEs and related topics” (Università degli Studi di Bari, May 2017).
   Google Scholar
• Fall M, Felli V. Unique continuation property and local asymptotics of solutions of frac- tional elliptic equations. Commun Partial Differ Equ. 2014;39(2):354–397. doi: 10.1080/03605302.2013.825918
   Web of Science ®Google Scholar
• Armstrong S, Silvestre L. Unique continuation for fully nonlinear elliptic equations. Math Res Lett. 2011;18:921–926. doi: 10.4310/MRL.2011.v18.n5.a9
   Web of Science ®Google Scholar
• Hui Y. Unique continuation for fractional orders of Elliptic equations. Ann PDE. 2017;3(2):22.
   Google Scholar
• Seo I. Carleman inequalities for fractional Laplacians and unique continuation. Taiwanese J Math. 2015;19(5):1533–1540. doi: 10.11650/tjm.19.2015.5624
   Web of Science ®Google Scholar
• Chua SK. Extension theorems on weighted Sobolev spaces. Indiana Univ Math J. 1992;41(4):1027–1076. doi: 10.1512/iumj.1992.41.41053
   Web of Science ®Google Scholar
• Dipierro S, Valdinoci E. A density property for fractional weighted Sobolev spaces. Atti Accad Naz Lincei Rend Lincei Mat Appl. 2015;26(4):397–422. doi: 10.4171/RLM/712
   Google Scholar
• Reed M, Simon B. Methods of modern mathematical physics. New York: Academic Press; 1978.
   Google Scholar
• Froese R, Herbest I, Hoffman-Ostenhoff M, et al. L2-Lower bounds to solutions of one-Body Schrödinger equations. Proc Roy Soc Edinburgh Sect A. 1983;95(1–2):25–38. doi: 10.1017/S0308210500015778
   Google Scholar