Nonlocal variational problems arising in long wave propagation
ESAIM: Control, Optimisation and Calculus of Variations, Tome 5 (2000), pp. 501-528.
@article{COCV_2000__5__501_0,
     author = {Lopes, Orlando},
     title = {Nonlocal variational problems arising in long wave propagation},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {501--528},
     publisher = {EDP-Sciences},
     volume = {5},
     year = {2000},
     mrnumber = {1799328},
     zbl = {0969.35046},
     language = {en},
     url = {http://archive.numdam.org/item/COCV_2000__5__501_0/}
}
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Lopes, Orlando. Nonlocal variational problems arising in long wave propagation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 5 (2000), pp. 501-528. http://archive.numdam.org/item/COCV_2000__5__501_0/

[1] R. Adams, Sobolev Spaces. Academic Press ( 1975). | MR | Zbl

[2] J. Albert, Concentration-Compactness and stability-wave solutions to nonlocal equations. Contemp. Math. 221, AMS ( 1999) 1-30. | MR | Zbl

[3] J. Albert, J. Bona and D. Henry, Sufficient conditions for stability of solitary-wave solutions of model equations for long waves. Phys. D 24 ( 1987) 343-366. | MR | Zbl

[4] J. Albert, J. Bona and J.C. Saut, Model equations for waves in stratified fluids. Proc. Roy. Soc. London Ser. A 453 ( 1997) 1233-1260. | MR | Zbl

[5] J. Bergh and J. Lofstrom, Interpolation Spaces. Springer-Verlag, New-York/Berlin ( 1976). | MR | Zbl

[6] P. Blanchard and E. Bruning, Variational Methods in Mathematical Physics. Springer-Verlag ( 1992). | MR | Zbl

[7] H. Brezis and E. Lieb, Minimum Action Solutions of Some Vector Field Equations. Comm. Math. Phys. 96 ( 1984) 97-113. | MR | Zbl

[8] A. De Bouard, Stability and instability of some nonlinear dispersive solitary waves in higher dimension. Proc. Roy. Soc. Edinburgh Sect. A 126 ( 1996) 89-112. | MR | Zbl

[9] I. Catto and P.L. Lions, Binding of atoms and stability of molecules in Hartree and Thomas-Fermi type theories, Part I. Comm. Partial Differential Equations 17 ( 1992) 1051-1110. | MR | Zbl

[10] T. Cazenave and P.L. Lions, Orbital Stability of Standing waves for Some Nonlinear Schrödinger Equations. Comm. Math. Phys. 85 ( 1982) 549-561. | MR | Zbl

[11] S. Coleman, V. Glazer and A. Martin, Action Minima among to a class of Euclidean Scalar Field Equations. Comm. Math. Phys. 58 ( 1978) 211-221. | MR

[12] T. Colin and M. Weinstein, On the ground states of vector nonlinear Schrödinger equations. Ann. Inst. H. Poincaré Phys. Théor. 65 ( 1996) 57-79. | Numdam | MR | Zbl

[13] G.H. Derrick, Comments on Nonlinear Wave Equations as Models for Elementary Particles. J. Math. Phys. 5, 9 ( 1964) 1252-1254. | MR

[14] M. Grillakis, J. Shatah and W. Strauss, Stability of Solitary Waves in the Presence of Symmetry I. J. Funct. Anal. 74 ( 1987) 160-197. | MR | Zbl

[15] L. Hormander, Estimates for translation invariant operators in Lp spaces. Acta Math. 104 ( 1960) 93-140. | MR | Zbl

[16] O. Kavian, Introduction à la théorie des points critiques et applications aux problèmes elliptiques. Springer, Heidelberg ( 1993). | MR | Zbl

[17] P. Lax, Integrals of nonlinear equations of evolution and solitary waves. Comm. Pure Appl. Math. 21 ( 1968) 467-490. | MR | Zbl

[18] S. Levandosky, Stability and instability of fourth-order solitary waves. J. Dynam. Differential Equations 10 ( 1998) 151-188. | Zbl

[19] E. Lieb, Existence and uniqueness of minimizing solutions of Choquard's nonlinear equation. Stud. Appl. Math. 57 ( 1977) 93-105. | Zbl

[20] P.L. Lions, The Concentration-Compactness Principle in the Calculus of Variations. Ann. Inst. H. Poincaré Anal. Non Linéaire 1 ( 1984) Part I 109-145, Part II 223-283. | Numdam | Zbl

[21] P.L. Lions, Solutions of Hartree-Fock Equations for Coulomb Systems. Comm. Math. Phys. 109 ( 1987) 33-97. | Zbl

[22] O. Lopes, Radial symmetry of minimizers for some translation and rotation invariant functionals. J. Differential Equations 124 ( 1996) 378-388. | Zbl

[23] O. Lopes, Sufficient conditions for minima of some translation invariant functionals. Differential Integral Equations 10 ( 1997) 231-244. | MR | Zbl

[24] O. Lopes, A Constrained Minimization Problem with Integrals on the Entire Space. Bol. Soc. Brasil Mat. (N.S.) 25 ( 1994) 77-92. | MR | Zbl

[25] O. Lopes, Variational Systems Defined by Improper Integrals, edited by L. Magalhaes et al., International Conference on Differential Equations. World Scientific ( 1998) 137-153. | MR | Zbl

[26] O. Lopes, Variational problems defined by integrals on the entire space and periodic coefficients. Comm. Appl. Nonlinear Anal. 5 ( 1998) 87-120. | MR | Zbl

[27] J. Maddocks and R. Sachs, On the stability of KdV multi-solitons. Comm. Pure. Appl. Math. 46 ( 1993) 867-902. | MR | Zbl

[28] J.C. Saut, Sur quelques généralizations de l'équation de Korteweg-de Vries. J. Math. Pure Appl. (9) 58 ( 1979) 21-61. | MR | Zbl

[29] H. Triebel, Interpolation Theory, Functions Spaces, Differential Operators. North-Holland, Amsterdam ( 1978). | MR | Zbl

[30] M. Weinstein, Liapunov Stability of Ground States of Nonlinear Dispersive Evolution Equations. Comm. Pure Appl. Math. 39 ( 1986) 51-68. | MR | Zbl

[31] M. Weinstein, Existence and dynamic stability of solitary wave solution of equations arising in long wave propagation. Comm. Partial Differential Equations 12 ( 1987) 1133-1173. | MR | Zbl