Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Linking in Hilbert space

Authors: Martin Schechter and Kyril Tintarev
Journal: Proc. Amer. Math. Soc. 134 (2006), 403-410
MSC (2000): Primary 35J65, 58E05, 49J27
Published electronically: August 25, 2005
MathSciNet review: 2176008
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We present the most general definition of the linking of sets in a Hilbert space and, drawing on the theory given in earlier papers by Schechter and Tintarev, give a necessary and sufficient geometric condition for linking when one set is compact.

References [Enhancements On Off] (What's this?)

  • 1. A. Ambrosetti and V.C. Zelati, Periodic Solutions of Singular Lagrangian Systems, Birkhäuser, 1993. MR 1267225 (95b:58054)
  • 2. P. Bartolo, V. Benci and D. Fortunato, Abstract critical applications to some nonlinear problems with ``strong'' resonance at infinity, Nonlinear Analysis TMA, 7(1983) 981-1012. MR 0713209 (85c:58028)
  • 3. H. Brezis and L. Nirenberg, Remarks on finding critical points, Comm. Pure Appl. Math. 44(1991) 939-964. MR 1127041 (92i:58032)
  • 4. V. Benci and P.H. Rabinowitz, Critical point theorems for indefinite functionals, Invent. Math. 52(1979) 241-273. MR 0537061 (80i:58019)
  • 5. K.C. Chang, Infinite dimensional Morse theory and multiple solution problems, Birkhäuser, Boston, 1993. MR 1196690 (94e:58023)
  • 6. J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Springer-Verlag, 1989. MR 0982267 (90e:58016)
  • 7. L. Nirenberg, Variational and topological methods in nonlinear problems, Bull. Amer. Math. Soc. 4(1981) 267-302. MR 0609039 (83e:58015)
  • 8. P.H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, Conf. Board of Math. Sci. Reg. Conf. Ser. in Math. No. 65, Amer. Math. Soc. 1986. MR 0845785 (87j:58024)
  • 9. M. Schechter, The intrinsic mountain pass, Pacific J. Math., 171(1995) 529-544. MR 1372243 (97a:58032)
  • 10. M. Schechter, New linking theorems, Rend. Sem. Mat. Univ. Padova, 99(1998) 255-269.
  • 11. M. Schechter, Linking Methods in Critical Point Theory, Birkhäuser Boston, 1999. MR 1729208 (2001f:58032)
  • 12. S. Shi, Ekeland's variational principle and the mountain pass lemma. Acta Math. Sinica (N.S.) 1 (1985), no. 4, 348-355. MR 0867907 (87m:49039)
  • 13. E.A. de B.e. Silva, Linking theorems and applications to semilinear elliptic problems at resonance, Nonlinear Analysis TMA 16(1991) 455-477. MR 1093380 (92d:35108)
  • 14. M. Schechter and K. Tintarev, Pairs of critical points produced by linking subsets with applications to semilinear elliptic problems, Bull. Soc. Math. Belg. 44(1992) 249-261. MR 1314040 (95k:58033)
  • 15. K. Tintarev, Isotopic linking and critical points of functionals. Proceedings of the Second World Congress of Nonlinear Analysts, Part 7 (Athens, 1996). Nonlinear Anal. 30 (1997), no. 7, 4145-4149. MR 1603558 (99d:58037)
  • 16. M. Willem, Minimax Theorems, Birkhäuser, 1996. MR 1400007 (97h:58037)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35J65, 58E05, 49J27

Retrieve articles in all journals with MSC (2000): 35J65, 58E05, 49J27

Additional Information

Martin Schechter
Affiliation: Department of Mathematics, University of California, Irvine, California 92697-3875

Kyril Tintarev
Affiliation: Department of Mathematics, Uppsala University, P.O. Box 480, 751 06 Uppsala, Sweden

Keywords: Critical point theory, variational methods, saddle point theory
Received by editor(s): August 7, 2004
Published electronically: August 25, 2005
Additional Notes: The first author was supported in part by an NSF grant
The research was done while the second author was visiting UC Irvine; supported in part by a grant from the Swedish Research Council.
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society