Asymptotics for $L^2$ minimal blow-up solutions of critical nonlinear Schrödinger equation

 Access to full text

 Full (PDF)

1. [1] H. Berestycki and P.L. Lions, Nonlinear 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. Zbl0533.35029MR695535
2. [2] J. Ginibre and G. Velo, On a class of nonlinear Schrödinger equations I, II. The Cauchy problem, general case, J. Funct. Anal., Vol. 32, 1979, pp. 1-71. Zbl0396.35028MR533219
3. [3] T. Kato, On nonlinear Schrödinger equations, Ann. Inst. Henri Poincaré, Physique Théorique, Vol. 49, 1987, pp. 113-129. Zbl0632.35038MR877998
4. [4] M.K. Kwong, Uniqueness of positive solutions of Δu - u + up = 0 in RN, Arch. Rational Mech. Anal., Vol. 105, 1989, pp. 243-266. Zbl0676.35032MR969899
5. [5] F. Merle, Determination of blow-up solutions with minimal mass for Schrödinger equation with critical power, Duke J., Vol. 69, 1993, pp. 427-454. Zbl0808.35141MR1203233
6. [6] F. Merle, Nonexistence of minimal blow-up solutions of equations iut = -Δu - k(x)|u|4/Nu in RN, preprint. 
7. [7] W.A. Strauss, Existence of solitary waves in higher dimensions, Commun. Math. Phys., Vol. 55, 1977, pp. 149-162. Zbl0356.35028MR454365
8. [8] M.I. Weinstein, Modulational stability of ground states of the nonlinear Schrödinger equations, SIAM J. Math. Anal., Vol. 16, 1985, pp. 472-491. Zbl0583.35028MR783974
9. [9] M.I. Weinstein, Nonlinear Schrödinger equations and sharp interpolation estimates, Commun. Math. Phys., Vol. 87, 1983, pp. 567-576. Zbl0527.35023MR691044

1. Frank Merle, Recent progress on the blow-up problem of Zakharov equations
2. Mohammed Lemou, Florian Méhats, Pierre Raphaël, Uniqueness of the critical mass blow up solution for the four dimensional gravitational Vlasov–Poisson system
3. Nikolay Tzvetkov, On the long time behavior of KdV type equations
4. Valeria Banica, Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain