Bifurcation and Multiple Solutions for Perturbations of Linear Elliptic Problems

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.