Abstract
Let U(t, ) be solution of the Dirichlet problem
y''+( t-q(t))y= 0 - 1 t l
y(-l)= 0 = y(x),
with variabIe t on (-1, x), for fixed x, which satisfies the initial condition
U(-1, )=0 , (-1, )=1.
In this paper, the asymptotic representation of the corresponding eigenfunctions
of the eigen values has been investigated . Furthermore, the leading term of the
asymptotic formula for - (x, (x)), (x) and is obtained where (x) is a negative eigenvalue of the Dirichlet problem on [-1, x] with fixed x < 0.
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