In this paper.We mainly g(?)n(?)raliz(?) the H(?)lly lemma and application to proof the existence th or m of differential equation. Lemma.If F={f.x)}is a set of function of bound(?)d variation of order 2 and for every function f

x(?)hich satisfi s th(?) following conditions: 1|f(x)|≤(?); 2 (?)(f)≤K Where K is a finite Constant

Then from F may be determine a uniform con vergenc(?) s quence{f?

x)}.Which the Iimit function is a bounded variation function of order 2. Theorem 1.There is a problem (E:)d~2y/dx~2+P(x)dy/dx+Q(x)y=0. x=0

y=y0:dy/dx=(dy/dx)0. If P x Q(x)ar(?) bounded variation function of order 2 in the n(?)ighbor- hood of the initial point

Then E exist a solution of bounded variation order 3 in the neighborhood of the initial point. Th(?)or(?)m 2.If P(x)and Q(x) are L(?)bsgue integrable function at the neighbor-hood of the initial point

Th(?)n(E)has a solution of absolute function of order 2 at the neighborhood of the initial point.