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中文摘要：
应用锥理论和不动点指数方法，在与相应的线性算子第一特征值有关的条件下，获得了测度链上的非线性微分方程Lx（t）=-[τ（t）x^△（t）]^△=f（t，z（σ（t）））的正解的存在性．
英文摘要：
By applying the theory of fixed point index and the cone theory, the existence of positive solutions for the nonlinear differential equation on a measure chain Lx（t）=-[τ（t）x^△（t）]^△=f（t,z（σ（t））） is considered under some conditions concerning the first eigenvalue corresponding to the relevant linear operator.
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