@article{AIHPA_1996__64_1_33_0, author = {Merle, Frank}, title = {Nonexistence of minimal blow-up solutions of equations $iu\_t = - \Delta u-k(x)|u|^{4/N} u$ in $\mathbb {R}^N$}, journal = {Annales de l'I.H.P. Physique th\'eorique}, volume = {65}, year = {1996}, pages = {33-85}, zbl = {0846.35129}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPA_1996__64_1_33_0} }
Merle, Franck. Nonexistence of minimal blow-up solutions of equations $iu_t = - \Delta u-k(x)|u|^{4/N} u$ in $\mathbb {R}^N$. Annales de l'I.H.P. Physique théorique, Tome 65 (1996) pp. 33-85. http://gdmltest.u-ga.fr/item/AIHPA_1996__64_1_33_0/
[1] Non linear scalar field equations I. Existence of a ground state; II. Existence of infinitely many solutions, Arch. Rational Mech. Anal., Vol. 82, 1983, pp. 313-375. | Zbl 0533.35029
and ,[1'] The Cauchy problem in HS for nonlinear Schrödinger equation, preprint.
and ,[2] On a class of nonlinear Schrödingre equations I, II. The Cauchy problem, general case, J. Func. Anal., Vol. 32, 1979, pp. 1-71. | MR 533219 | Zbl 0396.35028
and ,[3] Existence of self-similar blow-up solutions for Zakharov equation in dimension two, Part I, Comm. Math. Phys., to appear. | MR 1262194 | Zbl 0808.35137
and ,[4] Concentration properties of blow-up solutions and instability results for Zakharov equation in dimension two, Part II, Comm. Math. Phys., to appear. | MR 1262202 | Zbl 0808.35138
and ,[5] On the blowing-up of solutions to the Cauchy problem for the nonlinear Schrödinger equation, J. Math. Phys., Vol. 18, 1977, pp. 1794-1797. | MR 460850 | Zbl 0372.35009
,[6] On nonlinear Schrödinger equations, Ann. Inst. Henri Poincaré, Physique Théorique, Vol. 49, 1987, pp. 113-129. | Numdam | MR 877998 | Zbl 0632.35038
,[7] Uniqueness of positive solution of Δu - u + up = 0 in RN, Arch. Rational Mech. Anal., Vol. 105, 1989, pp. 243-266. | MR 969899 | Zbl 0676.35032
,[8] Stability of isotropic self-similar dynamics for scalar collapse, Phys. Rev. A, Vol. 46, 1992, pp. 4869-7876.
, , , and ,[9] Limit behavior of satured approximations of nonlinear Schrödinger equation, Comm. Math. Phys., Vol. 149, 1992, pp. 377-414. | MR 1186035 | Zbl 0756.35094
,[9'] Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity, Comm. Math. Phys., Vol. 129, 1990, pp. 223-240. | MR 1048692 | Zbl 0707.35021
,[10] Determination of blow-up solutions with minimal mass for Schrödinger equation with critical power, Duke Math. J., Vol. 69, 1993, pp. 427-454. | MR 1203233 | Zbl 0808.35141
,[11] On uniqueness and continuation properties after blow-up time of self-similar solutions of nonlinear Schrödinger equation with critical exponent and critical mass, Comm. Pure Appl. Math., Vol. 45, 1992, pp. 203-254. | MR 1139066 | Zbl 0767.35084
,[12] L2-concentration of blow-up solutions for the non-linear Schrödinger equation with the critical power nonlinearity, J. Diff. Eq., Vol. 84, 1990, pp. 205-214. | MR 1047566 | Zbl 0722.35047
and ,[13] Blow-up for H1 solution for the nonlinear Schrödinger equation, preprint
and ,[14] Singular solutions of the Zakharov equations for Langmuir turbulence, Phys. Fluids B3, 1991, pp. 969-980. | MR 1097565
, , and ,[15] Character of the singularity and stochastic phenomena in self-focusing, Zh. Eksp. Theor. Fiz, Pis'ma Red, Vol. 14, 1971, pp. 390-393.
, and ,[16] Existence of solitary waves in hiher dimensions, Comm. Math. Phys., Vol. 55, 1977, p. 149-162. | MR 454365 | Zbl 0356.35028
,[17] The nonlinear Schrödinger equation singularity formation stability and dispersion, AMS-SIAM Conference on the Connection between Infinite Dimensional and Finite Dimensional Dynamical Systems, July 1987. | Zbl 0703.35159
,[18] Nonlinear Schrödinger equations and sharp interpolation estimates, Comm. Math. Phys., Vol. 87, 1983, pp. 567-576. | MR 691044 | Zbl 0527.35023
,[19] On the structure and formation of singularities in solutions to the nonlinear dispersive evolution equations, Comm. Partial Diff. Eq., Vol. 11, 1986, pp. 545-565. | MR 829596 | Zbl 0596.35022
,