Multiple positive solutions of Hammerstein integral equations and applications to periodic boundary value problems

摘要

New results on the existence of multiple positive solutions of a Hammerstein integral equation of the formz(t)=∫Gk(t,s)f(s,z(s))ds≡Az(t)are obtained, where f may have singularities in its first or second variable. These results generalize some previous results obtained by the author. Applications of these results are given to the existence of multiple positive solutions for singular first or second order differential equations with periodic boundary conditions. These results are often new and some of them improve many known results.