@article{TMF_2021_209_2_a2,
author = {V. B. Shakhmurov},
title = {Integral problem for {Schr\"odinger-type} equations with the~general elliptic part},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {243--257},
year = {2021},
volume = {209},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2021_209_2_a2/}
}
V. B. Shakhmurov. Integral problem for Schrödinger-type equations with the general elliptic part. Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 2, pp. 243-257. http://geodesic.mathdoc.fr/item/TMF_2021_209_2_a2/
[1] D. M. Ambrose, G. Simpson, “Local existence theory for derivative nonlinear Schrödinger equations with noninteger power nonlinearities”, SIAM J. Math. Anal., 47:3 (2015), 2241–2264 | DOI | MR
[2] A. Ashyralyev, A. Sirma, “Nonlocal boundary value problems for the Schrödinger equation”, Comput. Math. Appl., 55:3 (2008), 392–407 | DOI | MR
[3] J. Bourgain, Global Solutions of Nonlinear Schrödinger Equations, American Mathematical Society Colloquium Publications, 46, AMS, Providence, RI, 1999 | DOI | MR
[4] T. Cazenave, F. B. Weissler, “The Cauchy problem for the critical nonlinear Schrödinger equation in $H^s$”, Nonlinear Anal., 14:10 (1990), 807–836 | DOI | MR
[5] T. Cazenave, Semilinear Schrödinger Equations, Courant Lecture Notes in Mathematics, 10, AMS, Providence, RI, 2003 | DOI | MR
[6] L. Escauriaza, C. E. Kenig, G. Ponce, L. Vega, “Hardy's uncertainty principle, convexity and Schrödinger evolutions”, J. Eur. Math. Soc., 10:4 (2008), 883–907 | DOI | MR
[7] J. Ginibre, G. Velo, “Smoothing properties and retarded estimates for some dispersive evolution equations”, Commun. Math. Phys., 144:1 (1992), 163–188 | DOI | MR
[8] C. E. Kenig, F. Merle, “Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation”, Acta Math., 201:2 (2008), 147–212 | DOI | MR
[9] M. Keel, T. Tao, “Endpoint Strichartz estimates”, Amer. J. Math., 120:5 (1998), 955–980 | DOI | MR
[10] R. Killip, M. Visan, “Nonlinear Schrödinger equations at critical regularity”, Evolition Equations, Clay Mathematics Proceedings, 17, eds. D. Ellwood, I. Rodnianski, G. Staffilani, J. Wunsch, AMS, Providence, RI, 2013, 325–437
[11] S. A. Molchanov, B. R. Vainberg, “Schrödinger operators with matrix potentials. Transition from the absolutely continuous to the singular spectrum”, J. Funct. Anal., 215:1 (2004), 111–129 | DOI | MR
[12] T. Tao, Nonlinear Dispersive Equations. Local and Global Analysis, CBMS Regional Conference Series in Mathematics, 106, AMS, Providence, RI, 2006 | DOI | MR
[13] X. Liu, G. Simpson, C. Sulem, “Stability of solitary waves for a generalized derivative nonlinear Schrödinger equation”, J. Nonlinear Sci., 23:4 (2013), 557–583 | DOI | MR
[14] O. Veliev, Multidimensional Periodic Schrödinger Operator. Perturbation Theory and Applications, Springer Tracts in Modern Physics, 263, Springer, Cham, 2015 | DOI | MR
[15] L. Byszewski, V. Lakshmikantham, “Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space”, Appl. Anal., 40:1 (1990), 11–19 | DOI | MR
[16] O. Bolojan-Nica, G. Infante, R. Precup, “Existence results for systems with coupled nonlocal conditions”, Nonlinear Anal., 94 (2014), 231–242 | DOI | MR
[17] R. Bunoiua, R. Precup, “Vectorial approach to coupled nonlinear Schrödinger systems under nonlocal Cauchy conditions”, Appl. Anal., 95:4 (2016), 731–747 | DOI | MR
[18] D. G. Gordeziani, G. A. Avalishvili, “Nelokalnye po vremeni zadachi dlya uravnenii tipa Shredingera. I. Zadachi v abstraktnykh prostranstvakh”, Differents. uravneniya, 41:5 (2005), 670–677 | DOI | MR
[19] G. M. Lieberman, “Nonlocal problems for quasilinear parabolic equations in divergence form”, AIMS Proc., 2003{(Special)} (2003), 563–570 | DOI | MR
[20] L. Byszewski, “Strong maximum and minimum principles for parabolic problems with non-local inequalities”, Z. Angew. Math. Mech., 70:3 (1990), 202–206 | DOI | MR
[21] J. M. Chadam, H.-M. Yun, “Determination of an unknown function in a parabolic equation with the overspecified condition”, Math. Methods Appl. Sci., 13:5 (1990), 421–430 | DOI | MR
[22] J. Chabrowski, “On nonlocal problems for parabolic equations”, Nagoya Math. J., 93 (1984), 109–131 | DOI | MR
[23] A. A. Kerefov, “Nelokalnye kraevye zadachi dlya parabolicheskikh uravnenii”, Differents. uravneniya, 15:1 (1979), 74–78 | MR | Zbl
[24] Y. Lin, “Analytical and numerical solutions for a class of nonlocal nonlinear parabolic differential equations”, SIAM J. Math. Anal., 25:6 (1994), 1577–1594 | DOI | MR
[25] P. N. Vabischevich, “Nelokalnye parabolicheskie zadachi i obratnaya zadacha teploprovodnosti”, Differents. uravneniya, 17:7 (1981), 1193–1199 | MR
[26] V. S. Vladimirov, Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1979 | MR | Zbl
[27] J. Bergh, J. Löfström, Interpolation spaces. An introduction, Grundlehren der mathematischen Wissenschaften, 223, Springer, Berlin, 1976 | DOI | MR
[28] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, VEB Deutscher Verlag der Wissenschaften, Berlin, 1978 | DOI | MR
[29] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, 30, Princeton Univ. Press, Princeton, NJ, 1970 | MR
[30] C. D. Sogge, Fourier Integrals in Classical Analysis, Cambridge Tracts in Mathematics, 105, Cambridge Univ. Press, Cambridge, 1993 | DOI | MR