Abstract
This article is dealing with two theorems on nonlinear eigenvalue problems given by H.-P.Heinz in [2]: The theorem 3.6 on bifurcation at an eigenvalue of infinite multiplicity is shown to be empty. The theorem 3.7, concerning eigenvalue problems with a homogeneous nonlinearity, is considerably improved. This results follow easily from a classical theorem on eigenvectors of nonlinear completely continuous operators.
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Literatur
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HEINZ, H.-P.: Über das Verzweigungsverhalten eines nichtlinearen Eigenwertproblems in der Nähe eines unendlich vielfachen Eigenwertes der Linearisierung. Manuscripta Math.19, 105–132 (1976).
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Sarreither, P. Verzweigung an Eigenwerten unendlicher Vielfachheit-Bemerkungen zu einer Arbeit von H.-P.Heinz. Manuscripta Math 24, 449–451 (1978). https://doi.org/10.1007/BF01168886
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DOI: https://doi.org/10.1007/BF01168886