Opuscula Math. 31, no. 1 (2011), 61-74
http://dx.doi.org/10.7494/OpMath.2011.31.1.61
Opuscula Mathematica
Existence and uniqueness of anti-periodic solutions for a class of nonlinear n-th order functional differential equations
Abstract. In this paper, we use the method of coincide degree theory to establish new results on the existence and uniqueness of anti-periodic solutions for a class of nonlinear \(n\)-th order functional differential equations of the form \[x^{(n)}(t)=F(t, x_t, x^{(n-1)}_t, x(t), x^{(n-1)}(t), x(t-\tau(t)), x^{(n-1)}(t-\sigma(t))).\]
Keywords: anti-periodic solution, coincidence degree, nonlinear \(n\)-th-order equation, delay.
Mathematics Subject Classification: 34K13.
- Ling Liu
- Yunnan University, Department of Mathematics, Kunming, Yunnan 650091, P.R. China
- Yongkun Li
- Yunnan University, Department of Mathematics, Kunming, Yunnan 650091, P.R. China
- Received: 2010-04-18.
- Revised: 2010-06-03.
- Accepted: 2010-06-07.
