The existence of positive solutions of a class second-order singular super-linear m-point boundary value problems

摘要

The existence of solutions of second-order boundary value problems are concerned with various boundary conditions. Many scholars use a lot of ways to discuss the existence of solutions of second-order boundary value problems, for example, by using topological degree theory, partly ordered method and critical point theory, we can obtain the existence of multiple solutions of boundary problems; we discuss the existence of solutions in the case of the right part of the equation does not have continuity condition and the equation has upper and lower solutions; we discuss the boundary problems by using fixed point theorem in cones and coincidence degree theory. This thesis studies the existence of positive solutions of a class second-order singular superlinear multi-point boundary value problems: u"(t) = f(t,u{t)), t∈(0,l); au(0) -bu'(0) = 0, cu{1) + du'(l) =∑m-2i=1δiu(ζi) by using fixed point theorem in cones, we found a sufficient condition for the existence of positive solutions.