Abstract
Based on a variational approach, we prove that a second-order singular damped differential equation has at least one periodic solution when some reasonable assumptions are satisfied.
Highlights
1 Introduction The purpose of this paper is to study the existence of T-periodic solutions for secondorder singular damped differential equation u (t) + q(t)u (t) + f u(t) = g(t), ( . )
Admits a repulsive singularity at u =, which means that lim f (u) = –∞
Author details 1School of Management, Qingdao Huanghai University, Qingdao, 266427, China. 2Department of Mathematics, College of Science, Hohai University, Nanjing, 210098, China. 3Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, China
Summary
The purpose of this paper is to study the existence of T-periodic solutions for secondorder singular damped differential equation u (t) + q(t)u (t) + f u(t) = g(t),. ) reduces to the following singular differential equation:. The existence of T-periodic solutions for the following singular damped differential equation u (t) + q(t)u (t) + p(t)u(t) + f u(t) = g(t) was discussed in [ – ] by using the Leray-Schauder alternative principle or Schauder?s fixed point theorem.
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