@phdthesis{BJHTUP11_2001__0604__P0_0, author = {Mari\c{s}, Mihai}, title = {Sur quelques probl\`emes elliptiques non-lin\'eaires}, series = {Th\`eses d'Orsay}, publisher = {Universit\'e de Paris-Sud U.F.R. Scientifique d'Orsay}, number = {604}, year = {2001}, language = {fr}, url = {http://archive.numdam.org/item/BJHTUP11_2001__0604__P0_0/} }
Mariş, Mihai. Sur quelques problèmes elliptiques non-linéaires. Thèses d'Orsay, no. 604 (2001), 122 p. http://numdam.org/item/BJHTUP11_2001__0604__P0_0/
[1] Multidimensional solitons in shear flows of the boundary-layer type, Sov. Phys. Dokl. 37(12) (December 1992), pp. 575-578.
, and ,[2] Model equations for waves in stratified fluids, Proc. R. Soc. Lond. A, 453 (1997), pp. 1233-1260. | MR | Zbl | DOI
, and ,[3] Stability of soliton-like bubbles, Physica D. 34, 1989, pp. 240-254. | MR | Zbl | DOI
, , , ,[4] Soliton-like "bubbles" in a system of interacting bosons, Phys. Lett. A 128, 1988, pp. 52-56. | MR | DOI
, ,[5] Interactions of permanent waves of finite amplitude, J. Math. Phys., 43 (1964), pp. 309-313. | MR | Zbl | DOI
and ,[6] Nonlinear Scalar Field Equations, I: Existence of a Ground State, and II: Existence of Infinitely Many Solutions, Arch. Rational Mech. Anal. 82, 1983, pp. 313-375. | MR | Zbl | DOI
, ,[7] An ODE approach to the existence of positive solutions for semilinear problems in , Indiana Univ. Math. J. 30, 1981, pp. 141-167. | MR | Zbl | DOI
, , ,[8] Interpolation Spaces, Springer-Verlag, Berlin 1976. | MR | Zbl | DOI
and ,[9] Integral representations of functions and imbedding theorems, Vol. I, Wiley, New York, 1978.
, and ,[10] Ginzburg-Landau vortices, PNLDE 13, Birkhäuser, Boston, 1994. | MR | Zbl
, , ,[11] Travelling waves for the Gross-Pitaevskii equation I, Ann. Inst. Henri Poincaré, Physique Théorique, Vol. 70, No. 2, 1999, pp. 147-238. | MR | Zbl | Numdam
, ,[12] Decay and analyticity of solitary waves, J. Math. Pures Appl., 76 (1997), pp. 377-430. | MR | Zbl | DOI
and ,[13] Instability of stationary bubbles, SIAM J. Math. Anal. 26, May 1995, No. 3, pp. 566-582. | MR | Zbl | DOI
,[14] Solitary waves of the generalized Kadomtsev-Petviashvili equations, Annales de l'Institut Henri Poincaré, Analyse Non Linéaire, 4 (1997), pp. 211-236. | MR | Zbl | Numdam | DOI
and ,[15] Symmetries and decay of the generalized Kadomtsev-Petviashvili solitary waves, SIAM J. Math. Anal., Vol 28, No. 5, September 1997, pp. 1064-1085. | MR | Zbl | DOI
and ,[16] Lifting in Sobolev spces, Journal d'Analyse Mathématique, vol. 80, 2000, pp. 37-86. | MR | Zbl | DOI
, , ,[17] Remarks on the Schrödinger operator with singular complex potentials, J. Math. Pures et Appl., 58, 1979, pp. 137-151. | MR | Zbl
, ,[18] An introduction to nonlinear Schrödinger equations, third edition, Instituto de Matematica - UFRJ, Rio de Janeiro, 1996.
,[19] Bifurcation from simple eigenvalues, J. Funct. Anal. 8, 1971, pp. 321-340. | MR | Zbl | DOI
and ,[20] Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential, J. Funct. Anal. 69, 1986, pp. 397-408. | MR | Zbl | DOI
, ,[21] A general mountain pass principle for locating and classifying critical points, Ann. Inst. Henri Poincaré, Analyse non-linéaire, Vol. 6, No. 5, 1989, pp. 321-330. | MR | Zbl | Numdam | DOI
, ,[22] Motions in a Bose condensate III. The structure and effective masses of charged and uncharged impurities, J. Phys. A: Math., Nucl. Gen., Vol. 7, No. 2, 1974, pp. 260-279. | DOI
and ,[23] Nonlinear Schrödinger flow past an obstacle in one dimension, Physical Review E, Vol. 55, No. 3, 1997, pp. 2835-2845. | DOI
,[24] Introduction à la théorie des points critiques et applications aux problèmes elliptiques, Springer-Verlag, 1993. | MR | Zbl
,[25] Uniqueness of positive radial solutions of , Arch. Rational Mech. Anal. 105, 1989, pp. 243-266. | MR | Zbl
,[26] Analyticity of solitary-wave solutions of model equations for long waves, SIAM J. Math. Anal., 27 (1996), pp. 725-737. | MR | Zbl | DOI
and ,[27] Analysis, Graduate Studies in Mathematics, Vol. 14, AMS, 1997. | MR
, ,[28] Slow travelling bubbles in two and three dimension, preprint, 1999.
,[29] Stability and instability of travelling solitonic bubbles, preprint, 1999. | MR | Zbl
,[30] Multipliers of Fourier integrals, Proc. Steklov Inst. Math., 89 (1967), pp. 269-290. | Zbl
,[31] Nonlocal variational problems arising in long wave propagation, ESAIM : Control, Optimization and Calculus of Variations, No. 5, 2000, pp. 501-528. | MR | Zbl | Numdam
,[32] Analyticity and decay properties of the solitary waves to the Benney-Luke equation, Differential and Integral Equations, Vol. 14, No. 3, March 2001, pp. 361-384. | MR | Zbl
,[33] On the existence, regularity and decay of solitary waves to a generalized Benjamin-Ono equation, to appear in Nonlinear Analysis TMA. | MR | Zbl | DOI
,[34] Stationary solutions to a nonlinear Schrödinger equation with potential in one dimension, to appear in Proc. Royal Soc. Edinburgh A. | MR | Zbl
,[35] Existence of nonstationary bubbles in higher dimensions, in preparation. | Zbl | DOI
,[36] Uniqueness of positive radial solutions of in , II, Transactions of the American Mathematical Society, Vol 339, No. 2, Oct. 1993, pp. 495-505. | MR | Zbl
,[37] Numerical study of hydrodynamics using the nonlinear Schrödinger equation, Physica D 65, 1993, pp. 154-162. | MR | Zbl | DOI
, , ,[38] The principle of symmetric criticality, Comm. Math. Phys. 69, 1979, 19-30. | MR | Zbl | DOI
,[39] Two dimensional solitary waves for a Benney-Luke equation, Physica D: Nonlinear Phenomena, No. 132, 1999, pp. 476-496. | MR | Zbl | DOI
, ,[40] Uniqueness of positive solutions of semilinear equations in , Arch. Rational Mech. Anal. 81, 1983, pp. 181-197. | MR | Zbl
, ,[41] Collapse transformation for self-focusing solitary waves in boundary-layer type shear flows, Physics Letters A, 206 (1995), pp. 195-202. | DOI
and ,[42] Some global results for nonlinear eigenvalue problems, J. Funct. Anal. 7, 1971, pp. 487-513. | MR | Zbl | DOI
,[43] Methods of Modern Mathematical Physics, vol. I and IV, Academic Press, New York, 1972-1979. | Zbl
, ,[44] Combinatorial identities, John Wiley & Sons, New York, 1968. | MR | Zbl
,[45] Fluid dynamical form of the linear and nonlinear Schrödinger equations, Physica D, Vol. 1, 1980, pp. 236-240. | MR | Zbl | DOI
,[46] Singular integrals and differentiability properties of functions, Princeton University Press, 1970. | MR | Zbl
,[47] Fourier Analysis on Euclidean Spaces, Princeton University Press, 1971. | MR | Zbl
, ,[48] Variational Methods, Springer-Verlag, 1996. | MR | DOI
,[49] Modulational stability of ground states of nonlinear Schrödinger equations, SIAM J. Math. Anal. 16, No. 3, May 1985, pp. 472-491. | MR | Zbl | DOI
,[50] Minimax Theorems, Progress in Nonlinear Differential Equations and their Applications, vol. 24, Birkhäuser, 1996. | MR | Zbl
,