An extension of the Rabinowitz bifurcation theorem to Lipschitz potential operators in Hilbert spaces
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- by Alexander Ioffe and Efim Schwartzman PDF
- Proc. Amer. Math. Soc. 125 (1997), 2725-2732 Request permission
Abstract:
The main result of the paper is an extension of the bifurcation theorem of Rabinowitz to equations $Ax + \varphi _\lambda (x) = \lambda x$ with $\varphi$ continuous jointly in $(\lambda ,x)$ and $\varphi _\lambda (\cdot )$ of class $C^{1,1}$. We also prove a bifurcation theorem for critical points of the function $g_{\lambda }(x)$ which is just continuous and changes at $x=0$ an isolated minimum (in $x$) to isolated maximum when $\lambda$ 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.References
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Additional Information
- Alexander Ioffe
- Affiliation: Department of Mathematics The Technion Haifa 32000, Israel
- MR Author ID: 91440
- Email: ioffe@math.technion.ac.il
- Efim Schwartzman
- Affiliation: Department of Mathematics The Technion Haifa 32000, Israel
- 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
- © Copyright 1997 American Mathematical Society
- 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