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Mathematics - Dynamical Systems & Differential Equations | Differential Equations with Operator Coefficients - with Applications to Boundary Value Problems

Differential Equations with Operator Coefficients

with Applications to Boundary Value Problems for Partial Differential Equations

Kozlov, Vladimir, Maz'ya, Vladimir

1999, XX, 444 p.

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* The aim of this book is to give a self-contained presentation of a theory of ordinary differential equations with unbounded operator coefficients in a Hilbert or Banach space. This theory has been developed over the last ten years by the authors. We study equations of the form t L{t, Dt)u{t) := L At-q{t)Dlu{t) = f{t) (0.1) q=O on the real axis lR or semiaxis t > to, where u and f are vector-valued functions and Dt = -i8t. We deal with the following topics • conditions of solvability • classes of uniqueness • estimates for solutions • asymptotic representations of solutions as t ---+ 00 Equations of the form (0.1) have numerous applications, especially to the theory of partial differential equations, and our exposition of abstract results is accompanied by many new applications to this theory. * The roots of the theme treated here are the qualitative and asymp­ totic theories of linear ordinary differential equations; these date back to Liouville, Sturm, Green, Stokes, Poincare, Lyapunov, to name only a few. In the twentieth century, fundamental contributions to the asymptotic analysis of ordinary differential equations were made by Birkhoff, Perron, Wentzel, Kramers, Brillouin and their numerous successors.

Content Level » Research

Keywords » Banach Space - Boundary value problem - Differential operator - Eigenvalue - Ordinary differential equations with operator coefficients - asymptotics of solutions - differential equation - ordinary differential equation - partial di - partial differential equation

Related subjects » Dynamical Systems & Differential Equations

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