Palais-Smale sequence relative to the Trudinger-Moser inequality

Calculus of Variations and Partial Differential Equations

Volumn 17, Issue 3, 2003, Pages 235-255

  Ohtsuka, Hiroshi ^a   Suzuki, Takashi ^b  

^a KISARAZU NATIONAL COLLEGE OF TECHNOLOGY   (Japan)

^b OSAKA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038675138     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00526-002-0168-7     Document Type: Article

References (34)

1. T. Aubin, Some Nonlinear Problems in Riemannian Geometry, Springer: New York, 1998
2. C. Bandle, Isoperimetric Inequalities and Applications, Pitman: London, 1980
3. u in two dimensions, Comm. Partial Differential Equations 16 (1991), 1223-1253
4. 1, J. Math. Soc. Japan 25 (1973) 565-590
5. E. Caglioti, P.L. Lions, C. Marchioro, M. Pulvirenti, A special class of stationary flows for two-dimensional Euler equations: a statistical mechanics description, Comm. Math. Phys. 143 (1992), 501-525
6. E. Caglioti, P.L. Lions, C. Marchioro, M. Pulvirenti, A special class of stationary flows for two-dimensional Euler equations: a statistical mechanics description. Part II, Comm. Math. Phys. 174 (1995), 229-260
7. 2, Acta Math. 159 (1987), 215-259
8. 2, J. Differential Geometry 27 (1988), 259-296
9. C.C. Chen, C.-S. Lin, On the symmetry of blowup solutions to a mean field equation, Ann. Inst. H. Poincaré Analyse Nonlinéaire 18 (2001), 271-296
10. 2u in dimension two, Comm. Anal. Geom. 7 (1999), 295-302
11. S. Childress, J.K. Percus, Nonlinear aspects of chemotaxis, Math. Biosci. 56 (1981), 217-237
12. W. Ding, J. Jost, J. Li, G. Wang, Existence results for mean field equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999), 653-666
13. L. Jeanjean, J.F. Tolland, Bounded Palais-Smale mountain-pass sequences, C. R. Acad. Sci. Paris, Ser. 1327 (1998), 23-28
14. J. Kazdan, F. Warner, Curvature functions for compact 2-manifolds, Ann. Math. 99 (1974), 14-47
15. E.F. Keller, L.A. Segel, Initiation of slime mold aggregation viewd as an instability, J. Theor. Biol. 26 (1970), 399-415
16. M.K.-H. Kiessling, Statistical mechanics of classical particles with logarithmic interactions, Comm. Pure Appl. Math. 46 (1993), 27-56
17. Y.Y. Li, Harnack type inequality: the method of moving planes, Comm. Math. Phys. 2000 (1999), 421-444
18. u in dimension two, Indiana Univ. Math. J. 43 (1994), 1255-1270
19. L. Ma, J.C. Wei, Convergence of a Liouville equation, preprint
20. J. Moser, A sharp form of an inequality by N. Trudinger, Indiana Univ. Math. J. 20 (1971), 1077-1092
21. J. Moser, On a nonlinear problem in differential geometry, In: Dynamical Systems (M. Peixoto: ed.), pp. 273-280, Academic Press: New York, 1973
22. K. Nagasaki, T. Suzuki, Asymptotic analysis for two-dimensional elliptic eigenvalue problems with exponentially-dominated nonlinearities, Asymptotic Analysis 3 (1990), 173-188
23. M. Nolasco, G. Tarantello, On a sharp Sobolev-type inequality on two-dimensional compact manifolds, Arch. Rational Mech. Anal. 145 (1998), 161-195
24. T. Ogawa, A proof of Trudinger's inequality and its application to nonlinear Schrödinger equations, Nonl. Anal. 14 (1990), 765-769
25. X. Ren, J. Wei, On a two-dimensional elliptic problem with large exponent in nonlinearity, Trans. Amer. Math. Soc. 343 (1994), 749-763
26. T. Senba, T. Suzuki, Some structures of the solution set for a stationary system of chemotaxis, Adv. Math. Sci. Appl. 10 (2000), 191-224
27. T. Senba, T. Suzuki, Chemotactic collapse in a parabolic - elliptic system of mathematical biology, Adv. Differential Equations 6 (2001), 21-50
28. T. Senba, T. Suzuki, Time global solutions to a parablic-elliptic system modelling chemotaxis, preprint
29. E.M. Stein, Note on the class L log L, Studia Math. 32 (1969), 305-310
30. M. Struwe, G. Tarantello, On multivortex solutions in Chern-Simons-Higgs gauge theory, Boll. Unione Math. Ital. Sez. B (8) 1 (1998), 109-121
31. T. Suzuki, A note on the stability of stationary solutions to a system of chemotaxis, Communications in Contemporary Mathematics 2 (2000), 373-383
32. T. Suzuki, Semilinear Elliptic Equations, Gakkotosho: Tokyo, 1994
33. G. Tarantello, Multiple condensate solutions for the Chern-Simons-Higgs theory, J. Math. Phys. 37 (1996), 3769-3796
34. D. Ye, Une remarque sur le comportement asymptotique des solutions de Δu = λf(u), C. R. Acad. Sci. Paris, 325-I (1997), 1279-1282