Multiple solutions for the Brezis-Nirenberg problem

Advances in Differential Equations

Volumn 10, Issue 4, 2005, Pages 463-480

  Clapp, Mónica ^a   Weth, Tobias ^b  

^a UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

^b JUSTUS LIEBIG UNIVERSITY   (Germany)

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[No Author keywords available]

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EID: 33745689269     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. Th. Aubin, Problèmes isopérimétriques et espaces de Sobolev, J. Diff. Geom. 11 (1976), 573-598.
2. Th. Bartsch and M. Clapp, Critical point theory for indefinite functionals with symmetries, J. of Funct. Anal. 138 (1996), 107-136.
3. Th. Bartsch and T. Weth, A note on additional properties of sign changing solutions to superlinear elliptic equations, 22 (2003), 1-14
4. F. Bernis, J. García-Azorero, and I. Peral, Existence and multiplicity of nontrivial solutions in semilinear critical problems of fourth order, Adv. in Differential Equations 1, 219-240
5. H. Brezis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Commun. Pure Appl. Math. 36 (1983), 437-477.
6. A. Castro, J. Cossio, and J.M. Neuberger, A sign changing solution for a superlinear Dirichlet problem, Rocky Mountain J. Math. 27 (1997), 1041-1053.
7. A. Capozzi, D. Fortunato, and G. Palmieri, An existence result for nonlinear elliptic problems involving critical Sobolev exponent, Ann. Inst. H. Poincaré, Anal. Non Linéaire 2 (1985), 463-440.
8. G. Cerami, D. Fortunato, and M. Struwe, Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents, Ann. Inst. H. Poincaré, Anal. Non Linéaire 1 (1984), 341-350.
9. G. Cerami, S. Solimini, and M. Struwe, Some existence results for superlinear elliptic boundary value problems involving critical exponents, J. Funct. Anal. 69 (1986), 289-306.
10. M. Clapp and D. Puppe, Critical point theory with symmetries, J. reine angew. Math. 418 (1991), 1-29.
11. K. Deimling, Ordinary differential equations in Banach spaces, Lect. Notes. Math. 596, Springer-Verlag, Berlin-Heidelberg-New York 1977.
12. G. Devillanova and S. Solimini, Concentration estimates and multiple solutions to elliptic problems at critical growth, Adv. Diff. Eq. 7 (2002), 1257-1280.
13. G. Devillanova and S. Solimini, A multiplicity result for elliptic equations at critical growth in low dimension, Comm. Contemp. Math. 5 (2003), 171-177.
14. D.E. Edmunds, D. Fortunato, and E. Janelli, Critical exponents, critical dimensions and the biharmonic operator, Arch. Rational Mech. Anal. 112 (1990), 269-289
15. F. Gazzola, Critical growth problems for polyharmonic operators, Proc. Roy. Soc. Edinburgh 128A (1998), 251-263.
16. F. Gazzola, H.-C. Grunau, and M. Squassina, Existence and nonexistence result for critical growth biharmoic equations, Calc. Var. Partial Differential Equations 18 (2003), 117-143.
17. H. Grunau and G. Sweers, Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions, Math. Ann. 307 (1997), 588-626
18. E. Mitidieri, A Rellich type identity and applications, Comm. Partial Differential Equations 18 (1993), 125-151.
19. 2*-1 = 0, Top. Meth. Nonl. Anal. 3 (1994), 27-54.
20. P. Pucci and J. Serrin, Critical exponents and critical dimensions for polyharmonic operators, J. Math. Pures Appl. 69 (1990), 55-83
21. M. Struwe, Variational Methods. Applications to nonlinear partial differential equations and Hamiltonian systems, Springer-Verlag, Berlin-Heidelberg 1990.
22. G. Talenti, Best constant in Sobolev inequality, Ann. Mat. Pure Appl. 110 (1976), 353-372.
23. G. Tarantello, Nodal solutions of semilinear elliptic equations with critical exponent, Differential and Integral Equations 5 (1992), 25-42.
24. R.C.A.M. van der Vorst, Fourth order elliptic equations with critical growth, C. R. Acad. Sci. Paris Sér. I Math 320 (1995), 295-299
25. M. Willem, Minimax theorems, PNLDE 24, Birkhäuser, Boston-Basel-Berlin 1996.
26. 4/N-2 = 0, Nonlinear Anal. TMA 13 (1989), 353-372.