An extension of the Rabinowitz bifurcation theorem to Lipschitz potential operators in Hilbert spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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An extension of the Rabinowitz bifurcation theorem to Lipschitz potential operators in Hilbert spaces

Authors:	Alexander Ioffe Efim Schwartzman

Institution:	Department of Mathematics The Technion Haifa 32000, Israel ; Department of Mathematics The Technion Haifa 32000, Israel

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 an isolated minimum (in ) 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.

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

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