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Mathematics - Dynamical Systems & Differential Equations | Theory of a Higher-Order Sturm-Liouville Equation

Theory of a Higher-Order Sturm-Liouville Equation

Series: Lecture Notes in Mathematics, Vol. 1659

Kozlov, Vladimir, Maz'ya, Vladimir

1997, XII, 144 p.

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  • About this book

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.

Content Level » Research

Keywords » Boundary value problem - Green's function - differential equation - ordinary differential equation - partial differential equation

Related subjects » Dynamical Systems & Differential Equations

Table of contents 

Basic equation with constant coefficients.- The operator M(? t ) on a semiaxis and an interval.- The operator M(? t )??0 with constant ?0.- Green's function for the operator M(? t )??(t).- Uniqueness and solvability properties of the operator M(? t ??(t).- Properties of M(? t ??(t) under various assumptions about ?(t).- Asymptotics of solutions at infinity.- Application to ordinary differential equations with operator coefficients.

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