Abstract
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, bya prioribounds essentially due to Gupta and by a Leray–Schauder degree computation.
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