Existence Of Positive Solutions Of Several Class Singular Super-linear Multi-point Boundary Value Problems

This thesis studies the existence of positive solutions of several class singular super-linear multi-point boundary value problems. At first, we discuss the existence of positive solutions of second-order singular super-linear m—point boundary value problems: u"(i) + f(t,u(t)) = 0,t∈(0,1), u(0) = 0, u(1) =Σ_i=1^m-2δ_iu(ζ_i), and the existence of positive solutions of the more general m—point boundary value problems: u"(t) + f(t,u(t)) = 0, t∈(0,1), au(0) - bu'(0) = 0, cu(1) + du'(1) =Σ_i=1^m-2δ_iu(ζ_i), by using fixed point theorem in cones, we found the sufficient and necessary condition for the existence of positive solutions of this two class boundary value problems, and a sufficient condition and a necessary condition for the existence of positive solutions. Second, we discuss a class fourth-order singular super-linear m-point boundary value problems: u⁽⁴⁾(t) = f(t,u(t),-u"(t)), 0 < t < 1, u(0) =0, u(1) =Σ_i=1^m-2α_iu(η_i), au"(0) - bu'"(0) = 0, cu"(1) + du'"(1) =Σ_i=1^m-2β_iu"(η_i), andwe give the criterion for the existence of positive solutions.