Hostname: page-component-76c49bb84f-7l7zb Total loading time: 0 Render date: 2025-07-09T12:09:56.464Z Has data issue: false hasContentIssue false
  • English
  • Français

Variational perturbative methods and bifurcation of bound states from the essential spectrum*

Published online by Cambridge University Press:  14 November 2011

Antonio Ambrosetti  and
Marino Badiale
Antonio Ambrosetti
Affiliation:
Scuola Normale Superiore, Pisa, 56100, Italy
Marino Badiale
Affiliation:
Scuola Normale Superiore, Pisa, 56100, Italy
Get access Rights & Permissions [Opens in a new window]

Extract

This paper consists of two main parts. The first deals with a perturbative method in critical point theory and can be seen as the generalisation and completion of some earlier results. The second part is concerned with applications of the abstract setup to the existence of bound states of a class of elliptic differential equations that branch off from the infimum of the essential spectrum.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 6 , 1998 , pp. 1131 - 1161
Copyright
Copyright © Royal Society of Edinburgh 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1Ambrosetti, A., Arcoya, D. and Gamez, J.. Asymmetric bound states of differential equations in nonlinear optics (to appear).Google Scholar
2Ambrosetti, A. and Badiale, M.. Homoclinics: Poincaré–Melnikov type results via a variational approach. Ann. Inst. H. Poincaré Anal. Non Linéaire (to appear); see also the preliminary Note, C. R. Acad. Sci. Paris Sér. I 323 (1996), 753é8.Google Scholar
3Ambrosetti, A., Badiale, M. and Cingolani, S.. Semiclassical states of nonlinear Schrödinger equations. Arch. Rational Mech. Anal, (to appear); see also the preliminary Note, Rend. Lincei. Ser.;IX 7 (1996), 155–60.Google Scholar
4Magnus, R. J.. On perturbations of translationally invariant differential equations. Proc. Roy. Soc. Edinburgh Sect. A 110 (1988), 1–25.CrossRefGoogle Scholar
5Stuart, C.. Bifurcation in L p(ℝN) for a semilinear elliptic equation. Proc. London Math. Soc. 57 (1988), 5–41.Google Scholar
6Stuart, C.. Bifurcation of homoclinic orbits and bifurcation from the essential spectrum. SIAM J. Math. Anal. 20(1989), 1145–71.CrossRefGoogle Scholar
7Stuart, C.. Bifurcation from the essential spectrum for some non-component non-linearities. Math. Methods Appl. Sci. 11 (1989), 525–42.CrossRefGoogle Scholar