Solutions in exterior domains of null mass nonlinear field equations

Advanced Nonlinear Studies

Volumn 6, Issue 2, 2006, Pages 171-198

  Benci, Vieri ^a   Micheletti, Anna Maria ^a  

^a UNIVERSITY OF PISA   (Italy)

Author keywords

Exterior domain; Nonlinear equation; Orlicz spaces; Variational methods

Indexed keywords

EID: 33744522162     PISSN: 15361365     EISSN: None     Source Type: Journal    
DOI: 10.1515/ans-2006-0204     Document Type: Article

References (30)

1. A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal.14 (1973), 349-381.
2. M. Badiale and S. Rolande, Elliptic problems with singular potential and double-power nonlinearity, preprint.
3. V. Benci and G. Cerami, Positive solutions of some non linear elliptic problem on exterior domain, Arch. Rational Mech. Anal. 99 (1987), 283-300.
4. V. Benci and D. Fortunate. A strongly degenerate elliptic equation arising from the semilinear maxwell equations, to appear in C. R. Math. Acad. Sci. Paris.
5. V. Benci and D. Fortunate. Towards a unified field theory for classical electrodynamics, to appear in Arch. Ration. Mech. Anal.
6. V. Benci, C.R. Grisanti and A.M. Micheletti Existence and non existence of the ground state solution for non linaer Schroedinger equations with V(∞) = 0, Topological Methods in Nonlinear Analysis 26, (no.2) (2005), 203-219.
7. V. Benci, C.R. Grisanti and A.M. Micheletti, Existence of solutions for nonlinear Schroedinger equations with V(∞) = 0, Nonlinear Differential Equations and Their Applications 68 (2005), 53-63.
8. H. Berestycki and P. L. Lions, Nonlinear scalar field Equations I. Existance of a ground state, Arch. Rational Mech. Anal. 82 (1983), 313-346.
9. H. Berestycki and P. L. Lions, Nonlinear scalar field Equations II. Existance of infinitely many solutions, Arch. Rational Mech. Anal. 82 (1983), 347-376.
10. J. Berg and J. Lofstrom, Interpolation Spaces, Springer Verlag, Berlin Heidelberg New York, 1976.
11. C.V. Coffman and M.M. Marcus, Existance theorems for superlinear alliptic Dirichlet problems in exterior domains, preprint.
12. 3 = 0 and a variational characterization of other solutions. Arch. Rational Mech. Anal. 46 (1972), 81-95.
13. J. M. Coron, Topologie te cas limite des injections de Sobolev, C. R. Acad. Sci. Paris 299 (1984), 209-212.
14. M. J. Esteban and P. L. Lions, Existence and non-existence results for semilinear elliptic problems in unbounded domains, Proc. Royal Edinbourgh Soc., 93 A (1982), 1-14.
15. M. Ghimenti and A.M. Micheletti, Minimal nodal solutions for Schroedinger equations with double power nonlinearity and V(∞) = 0, preprint.
16. M. Ghoussoub, Duality and Perturbation Methods in Critical Point Theory, Cambridge University Press, 1993.
17. B. Gidas, Bifurcation Phenomena in Mathematical Physics and Related Topics, Proceedings of the NATO Advanced Study Institute held at Cargèse, June 24 - July 7, 1979 (C. Bardos and D. Bessis eds.), NATO Advanced Study Institute Series. Ser. C, Mathematical and Physical Sciences 54, 1980.
18. B. Gidas, W.M. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68, n. 3 (1979), 209-243.
19. n, Mathematical Analysis and Applications, Part A, 7 A of Advances in Mathematics Supplementary Studies, Academic Press, 1981.
20. J. A. Hempel, Multiple solutions for a class of nonlinear boundary value problems, Indiana Univ. Math. J. 20 (1971), 983-996.
21. H. Hofer, Variational and topological methods in partially ordered Hubert spaces, Math. Ann. 261 (1982), 493-514.
22. P. L. Lions, The concentration-compactness principle in the Calculus of Variations - The locally compact case - Part I, Ann. Inst. H. Poincaré - Analyse Nonlineaire 1 (1984), 109-145.
23. P. L. Lions, The concentration-compactness principle in the Calculus of Variations -The locally compact case - Part II, Ann. Inst. H. Poincaré. Analyse Nonlineaire. 1 (1984), 223-283.
24. K. McLeod and J. Serrin Uniqueness of solutions of semilinear Poisson equations, Proc. Natl. Acad. Sci. U.S.A. 78 (1981), 6592-6595.
25. Z. Nehari, On a class of nonlinear second-order differential equations, Trans. Amer. Math. Soc. 95 (1960), 101-123.
26. L. Pisani, Remark on the sum of Lebesgue spaces, preprint.
27. S. I. Pohožaev, On the eigenfunctions of the equation Δu + λf(u) = 0, Dokl. Akad. Nauk SSSR165 (1965), 36-39.
28. Paul H. Rabinowitz, Minimax Methods in Critical Point Theory With Applications to Differential Equations, volume 65 of CBMS Regional Conference Series in Mathematics. Published for the Conference Board of the Mathematical Sciences, Washington, DC, 1986.
29. W. A. Strauss, Existence of solitary waves in higher dimensions, Comm. Math. Phys., 55 (1977), 149-162.
30. M. Struwe, A global compactness result for elliptic boundary value problems involving limiting nonlinearities, Math. Z., 187 (1984), 511-517.