Bifurcation and multiple solutions for perturbations of linear elliptic problems

[摘要] 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 apriori bounds essentially due to Gupta and by a Leray-Schauder degree computation. (C) 1997 Academic Press.

[发布日期] 1997-10-15