Twist periodic solutions of second order singular differential equations

Twin Positive Periodic Solutions of Second Order Singular Differential Systems

In this paper, we study positive periodic solutions to singular second order differential systems. It is proved that such a problem has at least two positive periodic solutions. The proof relies on a nonlinear alternative of Leray–Schauder type and on Krasnosel’skĭı fixed point theorem on compression and expansion of cones.

Recent Existence Results for Second-Order Singular Periodic Differential Equations

Positive Periodic Solution for Second-Order Singular Semipositone Differential Equations

and Applied Analysis 3

Limit Properties of Solutions of Singular Second-Order Differential Equations

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 suffi...

Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations