## Theory of a higher-order Sturm-Liouville equationThis 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. |

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### Contents

Basic Equation with Constant Coefficients | 1 |

The Operator Mdt on a Semiaxis and an Interval | 15 |

The Operator Mdt uo with Constant uo | 25 |

Copyright | |

6 other sections not shown

### Other editions - View all

Theory of a Higher-Order Sturm-Liouville Equation Vladimir Kozlov,Vladimir Maz'ya Limited preview - 2006 |

Theory of a Higher-Order Sturm-Liouville Equation Vladimir Kozlov,Vladimir Maz'ya No preview available - 2014 |

### Common terms and phrases

a+,a absolutely continuous absolutely converges Applying Lemma arbitrary positive arrive asymptotic boundary value problem Chapter complete the proof considered analogously convergent Corollary denote drfc eigenvalues equal equation 0.1 estimates for Green's Existence Theorem exists a solution following estimate holds gu(t Hence Hilbert spaces implies inequalities hold integers integral interval introduce the function J—oo Kozlov large positive number left-hand side Lemma Let m+ Let u satisfy liminf linear independent lower estimates m+,m m++m Maz'ya measurable function min{m+,m minimal at oo non-negative non-zero obtain operator coefficients operator M(dt order m+ ordinary differential equation Poisson's functions polynomial positive constants proof of Proposition Proposition 1.2.2 r)dr r)dx ra/m+ Remark right-hand side roots s)drds satisfies the equation satisfy 4.2 Sect semiaxis smooth function solution of 2.1 solution of 7.34 Sturm-Liouville Equation Suppose u+(t Uniqueness and Solvability uniqueness class valid X+(u X+(uj