IJPAM: Volume 62, No. 4 (2010)
AND EIGENVECTORS OF A SYSTEM OF SECOND
ORDER DIFFERENTIAL EQUATIONS WITH
A TURNING POINT
Department of Mathematics
269, Diamond Harbour Road, Thakurpukur, Kolkata, 700063, INDIA
e-mail: [email protected]
Abstract.The present paper deals with a system of second order differential equations with turning points.
In particular we consider the second order differential system
, , , and , , , , are real-valued functions having continuous second order derivatives at , , being a positive constant and , a real parameter.
We determine the asymptotic solutions for such a system for large values of
the parameter and apply these to determine the asymptotic
distributions of the eigenvalues and the asymptotic values of the
normalizing constants in two cases when the boundary conditions are: (i) the
Dirichlet and (ii) the Neumann.
Received: May 7, 2010
AMS Subject Classification: 35B40, 37K40
Key Words and Phrases: asymptotic solutions, turning points, Dirichlet boundary conditions, Neumann boundary conditions, normalizing constants
Source: International Journal of Pure and Applied Mathematics