Multiple eigenvalues for singular Hammerstein integral equations with applications to boundary value problems

摘要

New results on the existence of multiple positive eigenvalues for singular Hammerstein integral equations are obtained. The radius of the spectrum of a linear Hammerstein integral operator is first employed to obtain a better upper bound for the eigenvalues we seek. These results are applied to treat some second-order ordinary differential equations with two point, three point and some periodic boundary value problems.