Bifurcation from essential spectrum for an elliptic equation with general nonlinearity

Abstract

In this paper, based on some prior estimates, we show that the essential spectrum $\lambda =0$ is a bifurcation point for an superlinear elliptic equation with only local conditions, which generalizes a series of earlier results on an open problem proposed by C. A. Stuart in 1983 [Lecture Notes in Mathematics, 1017].

This paper has been accepted by Science China Mathematics