Bifurcation at isolated eigenvalues for some elliptic equations on ℝN

Abstract

This paper concerns the bifurcation of bound states uϵL2(RN) for a class of second-order nonlinear elliptic eigenvalue problems that includes cases which are already known to exhibit some surprising behaviour. By treating a larger class of nonlinearities we cover new cases such as a situation where there is no bifurcation at a simple isolated eigenvalue lying at the bottom of the spectrum of the linearization. As an application of recent work on bifurcation for problems that are only Hadamard differentiable, we also establish bifurcation at all isolated eigenvalues of odd multiplicity which are sufficiently far from the essential spectrum.