Multiple Periodic Solutions for a Class of Second-order Nonlinear Neutral Delay Equations
نویسندگان
چکیده
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 existence of periodic solutions of functional differential equations, previous authors have used,mainly, fixed point theory, coincidence degree theory, Fourier analysis, and so forth. They have rarely used critical point theory. In [5, 6], the authors obtained multiple periodic solutions for a class of retarded differential equations by means of critical point theory and Zp-group index theory. These results were obtained by reducing retarded differential equations to related ordinary differential equations. The purpose of this paper is to establish a variational framework with delayed variables for a class of neutral differential equations. Unlike the papers [5, 6], our approach enables us to obtain by critical point theory and Z2-group index theory the existence of
منابع مشابه
EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR NEUTRAL DIFFERANCE EQUATIONS WITH VARIABLE DELAY
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