This book develops a detailed theory of a generalized Sturm-Liouville Equation, which includes conditions of solvability, classes of uniqueness, positivity properties of solutions and Green's functions, asymptotic properties of solutions at infinity. Of independent interest, the higher-order Sturm-Liouville equation also proved to have important applications to differential equations with operator coefficients and elliptic boundary value problems for domains with non-smooth boundaries. The book addresses graduate students and researchers in ordinary and partial differential equations, and is accessible with a standard undergraduate course in real analysis.

Ordinary Differential Equations, Partial Differential Equations, Operator Theory For graduate students and mathematicians

Contents: Introduction.- Basic Equations with Constant Coefficients.- The operator M (dt) on a Semiaxis.- The operator M (dt) - w0 with Constant w0.- Green's Function for the Operator M (dt) - w (t).- Uniqueness and Solvability Properties of the Operator M (dt) - w (t).- Properties of M (dt) - w (t) under Various Assumptions about w (t).- Asymptotics of Solutions at Infinity.- Appendix: Application to Ordinary Differential Equation with Operator Coefficients.

1997 . XI, 140 pp.
ISBN 3-540-63065-1
Softcover
DM 44,-
Available

Book category: Monograph
Publication language English
(Lecture Notes in Mathematics. Eds.: A. Dold; F. Takens. Vol. 1659)

Last update: July 23, 1998
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