Multiplicity Of Positive Solutions To Second Order Singular Neumann Boundary Value Problems Of Differential Systems

This paper considers second order singular of differentia] systemsatisfies Neumann boundary value problemwhere ρ₁, ρ₂ are constants in (—∞,0)∪(0,(Ï€²/4)). The type of perturbations f_t(t,x,y), i=1, 2, we are mainly interested in is that f_i(t,x,y) has a singularity near (x, y) — (0, 0), although the main results of this paper apply also to more general type of perturbations. This paper is devoted to establish the multiplicity of positive solutions to second-order singular Neumann boundary value problems of differential systems. It is proved that such a problem has at least two positive solutions under our reasonable conditions. The existence of the first solution is obtained by using a nonlinear alternative of Leray-Schauder, and the second one is found by using a Krasnoselskii fixed point theorem in cones.