IJPAM: Volume 72, No. 4 (2011)
EIGENVECTORS OF A SYSTEM OF SECOND ORDER
DIFFERENTIAL EQUATIONS WITH
A TURNING POINT (EXTENSION-1)
Department of Mathematics
269, Diamond Harbour Road, Thakurpukur, Kolkata, 700 063, INDIA
Abstract. Consider the system of second order differential equation
where , , , , , , and , , , , are real-valued functions having continuous second order derivatives at x, , being a real constant and , a real parameter.
In the present paper we consider m, a negative real number and determine the asymptotic solutions alongwith their derivatives for such a system for large values of the parameter and apply these to determine the asymptotic expressions for the distribution of the eigenvalues and the normalized eigenvectors under the Dirichlet boundary conditions.
Received: June 1, 2011
AMS Subject Classification: 35B40, 37K40
Key Words and Phrases: asymptotic solutions, turning points, Dirichlet boundary conditions, normalized eigenvectors
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395