Multiple periodic solutions for a class of second-order nonlinear neutral delay equations

Multiple Periodic Solutions for a Class of Second-order Nonlinear Neutral Delay Equations

where τ, σ , and c are real constants with τ ≥ 0, σ ≥ 0, |c| < 1, g(t,x) is a T-periodic function for t > 0 and, for an arbitrary bounded domain D ⊂ R, g(t,x) is a Lipschitzfunction on [0,T]×D. Moreover, p ∈ C(R,R), p(t +T) = p(t) and ∫ T 0 p(t)dt = 0. They obtained sufficient conditions which guarantee the existence of at least one T-periodic solution for the above system. However, for the exi...

Uncountably many bounded positive solutions for a second order nonlinear neutral delay partial difference equation

In this paper we consider the second order nonlinear neutral delay partial difference equation $Delta_nDelta_mbig(x_{m,n}+a_{m,n}x_{m-k,n-l}big)+ fbig(m,n,x_{m-tau,n-sigma}big)=b_{m,n}, mgeq m_{0},, ngeq n_{0}.$Under suitable conditions, by making use of the Banach fixed point theorem, we show the existence of uncountably many bounded positive solutions for the above partial difference equation...

EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR NEUTRAL DIFFERANCE EQUATIONS WITH VARIABLE DELAY

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.

Multiple periodic solutions to a class of second-order nonlinear mixed-type functional differential equations

where τ, σ , and c are constants in R with τ ≥ 0, σ ≥ 0, |c| < 1, g(t,x) is a T(> 0)-periodic function in t > 0, and for an arbitrary bounded domain E ⊂ R, g(t,x) is a Lipschitz function in [0,T] × E, p ∈ C(R,R), p(t +T) = p(t), and ∫ T 0 p(t)dt = 0. They obtained some sufficient conditions to guarantee the existence, at least a T-periodic solution, for this system. But, for the existence of pe...