On Some Aspects of Oscillation Theory and Geometry
Aug 2013 · American Mathematical Soc.
Ebook
195
Pages
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About this ebook
The aim of this paper is to analyze some of the relationships between
oscillation theory for linear ordinary differential equations on the
real line (shortly, ODE) and the geometry of complete Riemannian
manifolds. With this motivation the authors prove some new results in
both directions, ranging from oscillation and nonoscillation
conditions for ODE's that improve on classical criteria, to estimates
in the spectral theory of some geometric differential operator on
Riemannian manifolds with related topological and geometric
applications. To keep their investigation basically self-contained, the
authors also collect some, more or less known, material which often
appears in the literature in various forms and for which they give, in
some instances, new proofs according to their specific point of view.
oscillation theory for linear ordinary differential equations on the
real line (shortly, ODE) and the geometry of complete Riemannian
manifolds. With this motivation the authors prove some new results in
both directions, ranging from oscillation and nonoscillation
conditions for ODE's that improve on classical criteria, to estimates
in the spectral theory of some geometric differential operator on
Riemannian manifolds with related topological and geometric
applications. To keep their investigation basically self-contained, the
authors also collect some, more or less known, material which often
appears in the literature in various forms and for which they give, in
some instances, new proofs according to their specific point of view.
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