Abstract
We present some recent existence results for second-order singular periodic differential equations. A nonlinear alternative principle of Leray-Schauder type, a well-known fixed point theorem in cones, and Schauder's fixed point theorem are used in the proof. The results shed some light on the differences between a strong singularity and a weak singularity.
Highlights
The main aim of this paper is to present some recent existence results for the positive T periodic solutions of second order differential equation xatxft, x e t, 1.1 where a t, e t are continuous and T -periodic functions
It is well known that second order singular differential equations describe many problems in the applied sciences, such as the Brillouin focusing system 1 and nonlinear elasticity 2
Because we mainly focus on the applications of topological methods to singular equations in this paper, here we try to give a brief sketch of this problem
Summary
Recent Existence Results for Second-Order Singular Periodic Differential Equations. We present some recent existence results for second-order singular periodic differential equations. A nonlinear alternative principle of Leray-Schauder type, a well-known fixed point theorem in cones, and Schauder’s fixed point theorem are used in the proof. The results shed some light on the differences between a strong singularity and a weak singularity.
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