Limit Properties of Solutions of Singular Second-Order Differential Equations
نویسندگان
چکیده
We discuss the properties of the differential equation u′′ t a/t u′ t f t, u t , u′ t , a.e. on 0, T , where a ∈ R\{0}, and f satisfies the Lp-Carathéodory conditions on 0, T × R2 for some p > 1. A full description of the asymptotic behavior for t → 0 of functions u satisfying the equation a.e. on 0, T is given. We also describe the structure of boundary conditions which are necessary and sufficient for u to be at least in C1 0, T . As an application of the theory, new existence and/or uniqueness results for solutions of periodic boundary value problems are shown.
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تاریخ انتشار 2009