%0 Journal Article %T A RESEARCH NOTE ON THE SECOND ORDER DIFFERENTIAL EQUATION %J Journal of Sciences, Islamic Republic of Iran %I University of Tehran %Z 1016-1104 %D 1999 %\ 09/01/1999 %V 10 %N 3 %P - %! A RESEARCH NOTE ON THE SECOND ORDER DIFFERENTIAL EQUATION %R %X 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. %U https://jsciences.ut.ac.ir/article_31434_5ea31294f7373e2dccbeebc62955df5e.pdf