Limit Properties of Solutions of Singular Second-Order Differential Equations
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
Boundary Value Problems 2009, 2009:905769 doi:10.1155/2009/905769Published: 29 June 2009
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.