An extension of the Rabinowitz bifurcation

theorem to Lipschitz potential operators

in Hilbert spaces

Authors:
Alexander Ioffe and Efim Schwartzman

Journal:
Proc. Amer. Math. Soc. **125** (1997), 2725-2732

MSC (1991):
Primary 58E05; Secondary 49K99

DOI:
https://doi.org/10.1090/S0002-9939-97-04061-6

MathSciNet review:
1415327

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Abstract | References | Similar Articles | Additional Information

Abstract: The main result of the paper is an extension of the bifurcation theorem of Rabinowitz to equations with continuous jointly in and of class . We also prove a bifurcation theorem for critical points of the function which is just continuous and changes at an isolated minimum (in ) to isolated maximum when passes, say, zero. The proofs of the theorems, as well as the the theorems themselves, are new, in certain important aspects, even when applied to smooth functions.

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Additional Information

**Alexander Ioffe**

Affiliation:
Department of Mathematics The Technion Haifa 32000, Israel

Email:
ioffe@math.technion.ac.il

**Efim Schwartzman**

Affiliation:
Department of Mathematics The Technion Haifa 32000, Israel

DOI:
https://doi.org/10.1090/S0002-9939-97-04061-6

Keywords:
Critical point,
$C^{1,
1}$-function,
bifurcation,
modulus of regularity,
Palais-Smail condition

Received by editor(s):
February 5, 1996

Additional Notes:
The research was supported by the US-Israel BSF grant 90-00455 and by the Israel Ministry of Science and Technology grant 3501–1–91

Communicated by:
Hal L. Smith

Article copyright:
© Copyright 1997
American Mathematical Society