Periodic solutions of nonlinear second-order differential equations with parameter

Almost Periodic Solutions of Second Order Nonlinear Differential Equations with Almost Periodic Forcing

ON THE PERIODIC SOLUTIONS OF A CLASS OF nTH ORDER NONLINEAR DIFFERENTIAL EQUATIONS *

The nth order differential equation x + c (t )x + ƒ( t,x) = e(t),n>3 is considered. Using the Leray-Schauder principle, it is shown that under certain conditions on the functions involved, this equation possesses a periodic solution.

Periodic solutions of second-order differential equations with multiple delays

* Correspondence: [email protected] School of Mathematical Science and Computing Technology, Central South University, Changsha 410075, P. R. China Full list of author information is available at the end of the article Abstract By using the critical point theory and S index theory, we obtain a new result for the existence and multiplicity of periodic solutions for a class of second-order...

Positive Solutions of Second Order Nonlinear Differential Equations with Periodic Boundary Value Conditions

Criteria are established for existence of positive solutions to the second order periodic boundary value problem −u(t) + pu(t) + p1u(t) = f(t, u), t ∈ I = [0, T ], u(0) = u(T ), u(0) = u(T ), where p ∈ R and p1 ≥ 0. The discussion is based on the fixed point index theory in cones. AMS Subject Classification: 34B18

Existence of Solutions for Second-Order Nonlinear Impulsive Differential Equations with Periodic Boundary Value Conditions

Impulsive differential equations, which arise in physics, population dynamics, economics, and so forth, are important mathematical tools for providing a better understanding of many real-world models, we refer to [1–5] and the references therein. About the applications of the theory of impulsive differential equations to different areas, for example, see [6–15]. Boundary value problems (BVPs) f...