Examples of bifurcation from a continuum of eigenvalues and from the continuous spectrum
Authors:
M. C. Jorge and A. A. Minzoni
Journal:
Quart. Appl. Math. 51 (1993), 37-42
MSC:
Primary 86A20; Secondary 58F40
DOI:
https://doi.org/10.1090/qam/1205934
MathSciNet review:
MR1205934
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Abstract: In this note we consider an example arising from a caricature of a geophysical problem where we show explicitly bifurcation from a continuum of eigen-values. Also we consider an example of bifurcation from the continuous spectrum for a simple integrodifferential equation.
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V. Benci and D. Fortunato, Does bifurcation from the essential spectrum occur?, Comm. Partial Differential Equations 6, 249–272 (1981)
B. Chen, M. C. Jorge, and A. A. Minzoni, Bifurcation of solutions for an inverse problem in potential theory, Stud. Appl. Math. 86, 31–51 (1992)
C. A. Stuart, Bifurcation from the essential spectrum, Lecture Notes in Math., vol. 1017, Springer, Berlin, 1983, pp. 575–596
C. A. Stuart, Bifurcation from the continuous spectrum in ${L^p}\left ( \mathbb {R} \right )$, Internat. Ser. Numerical Math., vol. 79, Birkhäuser-Verlag, Basel, 1987, pp. 307–318
C. A. Stuart, Self trapping of an electromagnetic field and bifurcation from the essential spectrum, Arch. Rational Mech. Anal. 113, 65–96 (1991)
J. Toland, Global bifurcation for Neumann problems without eigenvalues, J. Differential Equations 44, 82–110 (1982)
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© Copyright 1993
American Mathematical Society