Periodic Solutions for a Class of n-dimensional Prescribed Mean Curvature Equations

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In this paper, by using an extension of Mawhin’s continuation theorem and some analysis methods, we study the existence of periodic solutions for the following prescribed mean curvature system $$\frac{d}{{dt}}\varphi \left( {x'} \right) + \nabla W\left( x \right) = p\left( t \right),$$ where x ∊ ℝn, W ∊ C1(ℝn, ℝ), p ∊ C(ℝ, ℝn) is T-periodic and $$\varphi \left( x \right)\frac{x}{{\sqrt {1 + |x{|^2}} }}.$$