A second order differential equation of T. Otsuki

A RESEARCH NOTE ON THE SECOND ORDER DIFFERENTIAL EQUATION

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 ...

On Fuzzy Solution for Exact Second Order Fuzzy Differential Equation

In the present paper, the analytical solution for an exact second order fuzzy initial value problem under generalized Hukuhara differentiability is obtained. First the solution of first order linear fuzzy differential equation under generalized Hukuhara differentiability is investigated using integration factor methods in two cases. The second based on the type of generalized Hukuhara different...

Analytic Solutions of a Second-Order Functional Differential Equation

On Singular Solutions of a Second Order Differential Equation

In the paper, sufficient conditions are given under which all nontrivial solutions of (g(a(t)y))+r(t)f(y) = 0 are proper where a > 0, r > 0, f(x)x > 0, g(x)x > 0 for x 6= 0 and g is increasing on R. A sufficient condition for the existence of a singular solution of the second kind is given.

Linear Perturbations of a Nonoscillatory Second Order Differential Equation Ii

Let y1 and y2 be principal and nonprincipal solutions of the nonoscillatory differential equation (r(t)y′)′ + f(t)y = 0. In an earlier paper we showed that if ∫∞(f − g)y1y2 dt converges (perhaps conditionally), and a related improper integral converges absolutely and sufficently rapidly, then the differential equation (r(t)x′)′ + g(t)x = 0 has solutions x1 and x2 that behave asymptotically like...