Theory of a Higher-Order Sturm-Liouville Equation
Kozlov, Vladimir.
Theory of a Higher-Order Sturm-Liouville Equation [electronic resource] / by Vladimir Kozlov, Vladimir Maz'ya. - XII, 144 p. online resource. - Lecture Notes in Mathematics, 1659 0075-8434 ; . - Lecture Notes in Mathematics, 1659 .
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.
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.
9783540691228
10.1007/BFb0094700 doi
Differential equations, partial.
Partial Differential Equations.
QA370-380
515.353
Theory of a Higher-Order Sturm-Liouville Equation [electronic resource] / by Vladimir Kozlov, Vladimir Maz'ya. - XII, 144 p. online resource. - Lecture Notes in Mathematics, 1659 0075-8434 ; . - Lecture Notes in Mathematics, 1659 .
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.
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.
9783540691228
10.1007/BFb0094700 doi
Differential equations, partial.
Partial Differential Equations.
QA370-380
515.353