Spectral Analysis for a Singular Differential System with Integral Boundary Conditions - Sun, F.; Liu, Lishan; Zhang, Xinguang; Wu, Yong Hong (2016)
© 2016, Springer International Publishing.In this paper, by constructing a cone K1 × K2 in the Cartesian product space C[0, 1] × C[0, 1], and using spectral analysis of the relevant linear operator for the corresponding differential system, some properties of the first eigenvalue corresponding to the relevant linear operator are obtained, and the fixed-point index of nonlinear operator in the K1 × K2 is calculated explicitly and the existence of at least one positive solution or two positive solutions of the singular differential system with integral boundary conditions is established.