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Bifurcation and Multiple Solutions for Perturbations of Linear Elliptic Problems

✍ Scribed by Daxin Zhu; Yujun Yang; Zheyi Liu

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
204 KB
Volume
214
Category
Article
ISSN
0022-247X

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✦ Synopsis

Combining a bifurcation theorem with a local Leray᎐Schauder degree theorem of Krasnoselskii and Zabreiko in the case of a simple singular point, we obtain an existence result on the number of small solutions for a class of functional bifurcation equations. Since this result contains the information of local Leray᎐Schauder degree, we obtain new multiplicity results for the perturbations of second-order linear elliptic problems by unbounded nonlinearities as applications here, by a priori bounds essentially due to Gupta and by a Leray᎐Schauder degree computation.

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