Author | Skubachevskii, Alexander L. author |
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Title | Elliptic Functional Differential Equations and Applications [electronic resource] / by Alexander L. Skubachevskii |
Imprint | Basel : Birkhรคuser Basel, 1997 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-9033-5 |
Descript | X, 294 p. online resource |
I Boundary Value Problems for Functional Differential Equations in One Dimension -- 1 Ordinary Differential Equations with Nonlocal Boundary Conditions -- 2 Difference Operators in One Dimension -- 3 The Boundary Value Problem for the Differential-Difference Equation -- 4 Generalized and Classical Solutions -- 5 Applications to Control Systems with Delay -- 6 The Boundary Value Problem for the Differential-Difference Equation with Degeneration -- Notes -- II The First Boundary Value Problem for Strongly Elliptic Differential-Difference Equations -- 7 Some Geometrical Constructions -- 8 Difference Operators in the Multidimensional Case -- 9 Necessary and Sufficient Conditions for Strong Ellipticity -- 10 Solvability and Spectrum -- 11 Smoothness of Generalized Solutions in Subdomains -- 12 Smoothness of Solutions on a Boundary of Neighboring Subdomains -- 13 Elliptic Differential Equations with Nonlocal Conditions on Shifts of Boundary -- Notes -- III Applications to the Mechanics of a Deformable Body -- 14 The Elastic Model -- 15 Variational and Boundary Value Problems -- 16 Smoothness of Solutions -- 17 The One-Dimensional Case -- Notes -- IV Semi-Bounded Differential-Difference Operators with Degeneration -- 18 Self-Adjoint Extension of a Semi-Bounded Differential-Difference Operator -- 19 The Spectrum of Semi-Bounded Differential-Difference Operators -- 20 Smoothness of Solutions of Equations with Degeneration -- Notes -- V Nonlocal Elliptic Boundary Value Problems -- 21 Nonlocal Elliptic Problems with a Parameter -- 22 Elliptic Equations with Nonlocal Boundary Conditions in a Cylinder -- 23 Elliptic Differential-Difference Equations in a Cylinder -- 24 Applications to the Multidimensional Diffusion Processes -- 25 Elliptic Problems with Nonlocal Conditions near the Boundary and Feller Semigroups -- Notes -- A Linear Operators -- B Functional spaces -- C Elliptic Problems -- List of Symbols