一类具有强奇性的Sturm-iouville边值问题正解的存在性

The Existence of Positive Solutions for a Class of Sturm-Liouville Boundary Value Problem with Strong Singular

用构造算子的方法来处理具有混合型边值条件的Sturm-Liouville边值问题（BVP）。考虑当时间t=0，该边值问题具有强奇性的情况，仍能得到其正解的存在性。若存在t∈[0，1]，使得权P（t0）=0，则称该边值问题在t0点处具有奇性。主要讨论奇点出现在t0=0时的情况，当∫0^1dt/p（t）〈∞时，称该边值问题在t0=0具有弱奇性；如果∫0^1dt/p（t）=∞，称该边值问题在t0=0具有强奇性。

In this paper, by constructing the operator we deal with the Sturm-LiouviUe boundary value problem with mixed boundary conditions. We can still obtain the existence of positive solutions for the boundary value problem if the time t = 0 is strong singularity. Normally if it exits t0∈[ 0, 1 ], indefinite weight p （ t0 ） = 0, we call that Sturm-Liouville boundary problem is singular. In this paper,we mainly discuss the singularity at to =0,if ∫0^1dt/p（t）〈∞ ,the boundary problem is weak singular at t=0 ;if ∫0^1dt/p（t）=∞ ,the boundary problemis strong singular at t = O.