Theory of a Higher-Order Sturm-Liouville Equation

1. Front Matter

   Pages I-XI

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2. Basic equation with constant coefficients

   • Vladimir Kozlov, Vladimir Maz'ya

   Pages 1-14

3. The operator M(∂ _t ) on a semiaxis and an interval

   • Vladimir Kozlov, Vladimir Maz'ya

   Pages 15-24

4. The operator M(∂ _t )−ω₀ with constant ω₀

   • Vladimir Kozlov, Vladimir Maz'ya

   Pages 25-35

5. Green's function for the operator M(∂ _t )−ω(t)

   • Vladimir Kozlov, Vladimir Maz'ya

   Pages 37-45

6. Uniqueness and solvability properties of the operator M(∂ _t −ω(t)

   • Vladimir Kozlov, Vladimir Maz'ya

   Pages 47-80

7. Properties of M(∂ _t −ω(t) under various assumptions about ω(t)

   • Vladimir Kozlov, Vladimir Maz'ya

   Pages 81-110

8. Asymptotics of solutions at infinity

   • Vladimir Kozlov, Vladimir Maz'ya

   Pages 111-125

9. Application to ordinary differential equations with operator coefficients

   • Vladimir Kozlov, Vladimir Maz'ya

   Pages 127-136

10. Back Matter

    Pages 137-140

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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.

• Boundary value problem
• Green's function
• differential equation
• ordinary differential equation
• partial differential equation
• partial differential equations

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