IJPAM: Volume 78, No. 1 (2012)
AND EIGENVECTORS OF A SYSTEM OF SECOND ORDER
DIFFERENTIAL EQUATIONS WITH A TURNING POINT
Department of Mathematics
269, Diamond Harbour Road, Thakurpukur, Kolkata, 700 063, INDIA
Abstract. Consider the system of second order differential equation
and , , , , are real-valued continuously differentiable functions of x on .
In the present paper we assume that the elements of , i.e. , for
and are at least twice continuously differentiable on and determine the asymptotic solutions along with their derivatives for the system for large values of the parameter and finally apply these to determine the asymptotic expressions for the distribution of the eigenvalues and the normalized eigenvectors under the Dirichlet and Neumann boundary conditions.
Received: March 19, 2012
AMS Subject Classification: 35B40, 37K40
Key Words and Phrases: asymptotic solutions, turning points, Dirichlet and Neumann boundary conditions, normalized eigenvectors
Download paper from here.
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395