University of Tehran Journal of Sciences, Islamic Republic of Iran 1016-1104 10 3 1999 09 01 A RESEARCH NOTE ON THE SECOND ORDER DIFFERENTIAL EQUATION - 31434 EN Journal Article 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. https://jsciences.ut.ac.ir/article_31434_1f31606e625f642c0ed46405aada38a5.pdf