Open Access Research Article

Limit Properties of Solutions of Singular Second-Order Differential Equations

Irena Rachůnková1*, Svatoslav Staněk1, Ewa Weinmüller2 and Michael Zenz2

Author Affiliations

1 Department of Mathematical Analysis, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc, Czech Republic

2 Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstrasse 8-10, 1040 Wien, Austria

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Boundary Value Problems 2009, 2009:905769  doi:10.1155/2009/905769

Published: 29 June 2009

Abstract

We discuss the properties of the differential equation , a.e. on , where , and satisfies the -Carathéodory conditions on for some . A full description of the asymptotic behavior for of functions satisfying the equation a.e. on is given. We also describe the structure of boundary conditions which are necessary and sufficient for to be at least in . As an application of the theory, new existence and/or uniqueness results for solutions of periodic boundary value problems are shown.