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

Ling Liu
Yongkun Li

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.

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