A nonlinear elliptic equation with singular potential and applications to nonlinear field equations

Journal of the European Mathematical Society

Volumn 9, Issue 3, 2007, Pages 355-381

  Badiale, Marino ^a   Benci, Vieri ^b   Rolando, Sergio ^a  

^a UNIVERSITY OF TURIN   (Italy)

^b UNIVERSITY OF PISA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34250309636     PISSN: 14359855     EISSN: None     Source Type: Journal    
DOI: 10.4171/JEMS/83     Document Type: Article

References (34)

1. Ambrosetti, A., Felli, V., Malchiodi, A.: Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity. J. Eur. Math. Soc. 7, 117-144 (2005) Zbl 1064.35175 MR 2120993
2. Ambrosetti, A., Rabinowitz, P. H.: Dual variational methods in critical point theory and applications. J. Funct. Anal. 14, 349-381 (1973) Zbl 0273.49063 MR 0370183
3. Badiale, M., Benci, V., Rolando, S.: Solitary waves: physical aspects and mathematical results. Rend. Sem. Mat. Univ. Pol. Torino 62, 107-154 (2004) Zbl pre05121560 MR 2131956
4. Badiale, M., Rolando, S.: A note on nonlinear elliptic problems with singular potentials. Rend. Lincei Mat. Appl. 17, 1-16 (2006) Zbl pre05058596
5. Badiale, M., Rolando, S.: Elliptic problems with singular potential and double-power nonlinearity. Mediterr. J. Math. 2, 417-436 (2005) Zbl pre05058641 MR 2192523
6. Badiale, M., Tarantello, G.: A Sobolev-Hardy inequality with applications to a nonlinear elliptic equation arising in astrophysics. Arch. Ration. Mech. Anal. 163, 259-293 (2002) Zbl 1010.35041 MR 1918928
7. Benci, V.: Solitons and Bohmian mechanics. Discrete Contin. Dyn. Syst. 8, 303-317 (2002) Zbl 0994.35102 MR 1897685
8. Benci, V., D'Aprile, T.: The semiclassical limit of the nonlinear Schrödinger equation in a radial potential. J. Differential Equations 184, 109-138 (2002) Zbl 1060.35129 MR 1929149
9. Benci, V., Fortunato, D.: A strongly degenerate elliptic equation arising from the semilinear Maxwell equations. C. R. Math. Acad. Sci. Paris 339, 839-842 (2004) Zbl pre02137982 MR 2111719
10. Benci, V., Fortunato, D.: Towards a unified field theory for classical electrodynamics. Arch. Ration. Mech. Anal. 173, 379-414 (2004) Zbl 1065.78004 MR 2091510
11. Benci, V., Grisanti, C. R., Micheletti, A.M.: Existence and nonexistence of the ground state solution for the nonlinear Schrödinger equations with V (∞) = 0. Topol. Methods Nonlinear Anal. 26, 203-219 (2005) Zbl 1105.35112 MR 2197759
12. Benci, V., Micheletti, A. M.: Solutions in exterior domains of null mass nonlinear field equations. Adv. Nonlinear Stud. 6, 171-198 (2006) Zbl pre05039911 MR 2219834
13. Benci, V., Visciglia, N.: Solitary waves with non-vanishing angular momentum. Adv. Nonlinear Stud. 3, 151-160 (2003) Zbl 1030.35051 MR 1955598
14. Berestycki, H., Lions, P.-L.: Nonlinear scalar field equations. I. Existence of a ground state. Arch. Ration. Mech. Anal. 82, 313-345 (1983) Zbl 0533.35029 MR 0695535
15. Bergh, J., Löfström, J.: Interpolation Spaces. Springer, Berlin (1976). Zbl 0344.46071 MR 0482275
16. Brezis, H., Dupaigne, L., Tesei, A.: On a semilinear elliptic equation with inverse-square potential. Selecta Math. (N.S.) 11, 1-7 (2005) Zbl pre05024139 MR 2179651
17. Brezis, H., Vazquez, J. L.: Blow-up solutions of some nonlinear elliptic problems. Rev. Math. Univ. Complut. Madrid 10, 443-469 (1997) Zbl 0894.35038 MR 1605678
18. Chabrowski, J.: On the nonlinear Neumann problem involving the critical Sobolev exponent and Hardy potential. Rev. Mat. Complut. 17, 195-227 (2004) Zbl pre02113563 MR 2063949
19. D'Aprile, T.: On a class of solutions with non-vanishing angular momentum for nonlinear Schrödinger equations. Differential Integral Equations 16, 349-384 (2003) Zbl 1031.35130 MR 1947957
20. Dupaigne, L.: A nonlinear elliptic PDE with the inverse-square potential. J. Anal. Math. 86, 359-398 (2002) Zbl 1034.35043 MR 1894489
21. Dupaigne, L., Nedev, G.: Semilinear elliptic PDE's with a singular potential. Adv. Differential Equations 7, 973-1002 (2002) Zbl pre01977268 MR 1895114
22. Egnell, H.: Asymptotic results for finite energy solutions of semilinear elliptic equations. J. Differential Equations 98, 34-56 (1992) Zbl 0778.35009 MR 1168970
23. Felli, V., Terracini, S.: Elliptic equations with multi-singular inverse-square potentials and critical nonlinearity. Comm. Partial Differential Equations 31, 469-495 (2006) Zbl pre05025025 MR 2209764
24. Ferrero, A., Gazzola, F.: Existence of solutions for singular critical growth semilinear elliptic equations. J. Differential Equations 177, 494-522 (2001) Zbl 0997.35017 MR 1876652
25. Giaquinta, M.: Introduction to Regularity Theory for Nonlinear Elliptic Systems. Birkhäuser, Basel (1993) Zbl 0786.35001 MR 1239172
26. Jabri, Y.: The Mountain Pass Theorem. Cambridge Univ. Press, Cambridge (2003) Zbl 1036.49001 MR 2012778
27. Jannelli, E.: The role played by space dimension in elliptic critical problems. J. Differential Equations 156, 407-426 (1999) Zbl 0938.35058 MR 1705383
28. Kavian, O.: Introduction à la théorie des points critiques et applications aux problèmes elliptiques. Springer, Paris (1993) Zbl 0797.58005 MR 1276944
29. Pisani, L.: Remarks on the sum of Lebesgue spaces. Work in progress
30. Rǎdulescu, V., Smets, D., Willem, M.: Hardy-Sobolev inequalities with remainder terms. Topol. Methods Nonlinear Anal. 20, 145-149 (2002) Zbl 1033.35044 MR 1940535
31. Rolando, S.: Nonlinear elliptic equations with singular symmetric potentials. PhD Thesis, Dipartimento di Matematica, Univ. di Torino
32. Ruiz, D., Willem, M.: Elliptic problems with critical exponents and Hardy potentials. J. Differential Equations 190, 524-538 (2003) Zbl pre01929521 MR 1970040
33. Solimini, S.: A note on compactness-type properties with respect to Lorentz norms of bounded subsets of a Sobolev space. Ann. Inst. H. Poincaré Anal. Non Linéaire 12, 319-337 (1995) Zbl 0837.46025 MR 1340267
34. Willem, M.: Minimax Theorems. Progr. Nonlinear Differential Equations 24, Birkhäuser, Boston (1996) Zbl 0856.49001 MR 1400007