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1. | Department of Mathematics, and Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju 561-756 |
2. | Department of Mathematics, King Saud University, P.O. Box 2455, 11451 Riyadh, Saudi Arabia |
3. | Department of Mathematical Sciences, Seoul National University, Seoul 151-747, South Korea |
4. | Department of Applied Physics, Waseda University, Tokyo, 169-8555 |
References:
[1] |
J. P. Borgna and D. F. Rial, Existence of ground states for a one dimensional relativistic Schrodinger equations, J. Math. Phys., 53, 062301 (2012).
doi: 10.1063/1.4726198. |
[2] |
T. Cazenave, Semilinear Schrödinger Equations, Courant Lecture Notes in Mathematics, 10. New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2003. |
[3] |
Y. Cho, H. Hajaiej, G. Hwang and T. Ozawa, On the Cauchy problem of fractional Schrödinger equation with Hartree type nonlinearity, Funkcialaj Ekvacioj, 56 (2013), 193-224. |
[4] |
Y. Cho, G. Hwang and T. Ozawa, Global well-posedness of critical nonlinear Schrödinger equations below $L^2$, DCDS-A, 33 (2013), 1389-1405.
doi: 10.3934/dcds.2013.33.1389. |
[5] |
Y. Cho and S. Lee, Strichartz estimates in spherical coordinates,, to appear in \emph{Indina Univ. Math. J.}, ().
|
[6] |
Y. Cho and T. Ozawa, Sobolev inequalities with symmetry, Contem. Math., 11 (2009), 355-365.
doi: 10.1142/S0219199709003399. |
[7] |
Y. Cho, T. Ozawa and S. Xia, Remarks on some dispersive estimates, Commun. Pure Appl. Anal., 10 (2011), 1121-1128.
doi: 10.3934/cpaa.2011.10.1121. |
[8] |
Daoyuan Fang and Chengbo Wang, Weighted strichartz estimates with angular regularity and their applications, Forum Mathematicum, 23 (2011), 181-205.
doi: 10.1515/FORM.2011.009. |
[9] |
P. Felmer, A. Quaas and J. Tan, Positive solutions of nonlinear Schrödinger equation with the fractional Laplacian, P. Roy. Soc. Edinburgh A, 142 (2012), 1237-1262.
doi: 10.1017/S0308210511000746. |
[10] |
B. Guo and D. Huang, Existence and stability of standing waves for nonlinear fractional Schr\"odinger equations, J. Math. Phys., 53, 083702 (2012).
doi: 10.1063/1.4746806. |
[11] |
H. Hajaiej, Existence of minimizers of functionals involving the fractional gradient in the absence of compactness, symmetry and monotonicity, J. Math. Anal. Appl., 399 (2013), 17-26.
doi: 10.1016/j.jmaa.2012.09.023. |
[12] |
H. Hajaiej, L. Molinet, T. Ozawa and B. Wang, Necessary and sufficient conditions for the fractional Gargliardo-Nirenberg inequalities and applications to Navier-Stokes and generalized boson equations, RIMS Kokyuroku Bessatsu, B26 (2011), 159-199. |
[13] |
A. D. Ionescu and F. Pusateri, Nolinear fractional Schrödinger equations in one dimension,, \emph{To appear in J. Funct. Anal.}, ().
doi: 10.1016/j.jfa.2013.08.027. |
[14] |
P.-L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case. I, II, Ann. Inst. H. Poincare' Anal. Non Line'aire, 1 (1984), 109-145; 223-283. |
[15] |
T. Ozawa, Remarks on proofs of conservation laws for nonlinear Schrödinger equations, Cal. Var. PDE., 25 (2006), 403-408.
doi: 10.1007/s00526-005-0349-2. |
show all references
References:
[1] |
J. P. Borgna and D. F. Rial, Existence of ground states for a one dimensional relativistic Schrodinger equations, J. Math. Phys., 53, 062301 (2012).
doi: 10.1063/1.4726198. |
[2] |
T. Cazenave, Semilinear Schrödinger Equations, Courant Lecture Notes in Mathematics, 10. New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2003. |
[3] |
Y. Cho, H. Hajaiej, G. Hwang and T. Ozawa, On the Cauchy problem of fractional Schrödinger equation with Hartree type nonlinearity, Funkcialaj Ekvacioj, 56 (2013), 193-224. |
[4] |
Y. Cho, G. Hwang and T. Ozawa, Global well-posedness of critical nonlinear Schrödinger equations below $L^2$, DCDS-A, 33 (2013), 1389-1405.
doi: 10.3934/dcds.2013.33.1389. |
[5] |
Y. Cho and S. Lee, Strichartz estimates in spherical coordinates,, to appear in \emph{Indina Univ. Math. J.}, ().
|
[6] |
Y. Cho and T. Ozawa, Sobolev inequalities with symmetry, Contem. Math., 11 (2009), 355-365.
doi: 10.1142/S0219199709003399. |
[7] |
Y. Cho, T. Ozawa and S. Xia, Remarks on some dispersive estimates, Commun. Pure Appl. Anal., 10 (2011), 1121-1128.
doi: 10.3934/cpaa.2011.10.1121. |
[8] |
Daoyuan Fang and Chengbo Wang, Weighted strichartz estimates with angular regularity and their applications, Forum Mathematicum, 23 (2011), 181-205.
doi: 10.1515/FORM.2011.009. |
[9] |
P. Felmer, A. Quaas and J. Tan, Positive solutions of nonlinear Schrödinger equation with the fractional Laplacian, P. Roy. Soc. Edinburgh A, 142 (2012), 1237-1262.
doi: 10.1017/S0308210511000746. |
[10] |
B. Guo and D. Huang, Existence and stability of standing waves for nonlinear fractional Schr\"odinger equations, J. Math. Phys., 53, 083702 (2012).
doi: 10.1063/1.4746806. |
[11] |
H. Hajaiej, Existence of minimizers of functionals involving the fractional gradient in the absence of compactness, symmetry and monotonicity, J. Math. Anal. Appl., 399 (2013), 17-26.
doi: 10.1016/j.jmaa.2012.09.023. |
[12] |
H. Hajaiej, L. Molinet, T. Ozawa and B. Wang, Necessary and sufficient conditions for the fractional Gargliardo-Nirenberg inequalities and applications to Navier-Stokes and generalized boson equations, RIMS Kokyuroku Bessatsu, B26 (2011), 159-199. |
[13] |
A. D. Ionescu and F. Pusateri, Nolinear fractional Schrödinger equations in one dimension,, \emph{To appear in J. Funct. Anal.}, ().
doi: 10.1016/j.jfa.2013.08.027. |
[14] |
P.-L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case. I, II, Ann. Inst. H. Poincare' Anal. Non Line'aire, 1 (1984), 109-145; 223-283. |
[15] |
T. Ozawa, Remarks on proofs of conservation laws for nonlinear Schrödinger equations, Cal. Var. PDE., 25 (2006), 403-408.
doi: 10.1007/s00526-005-0349-2. |
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