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中文摘要：
研究非线性Neumann问题（p（t）u＇＋q（t）u=f（t,u）,t∈（0,1）,u＇（0）=u＇（1）=0正解的存在性，其中p,q∈C[0,1]满足p（t）〉0，0〈q（t）〈b＊，t∈[0，1]，b＊为线性问题（p（t）＇）＇＋bu=0,u＇（0）=0,u（1）=0的第一特征值．运用拓扑度理论及Rabinowitz全局分歧定理为上述问题建立了正解的存在性结果．
英文摘要：
We are concerned with the existence of positive solutions of the nonlinear Neumann problem （p（t）u＇＋q（t）u=f（t,u）,t∈（0,1）,u＇（0）=u＇（1）=0 where p,q∈C[0,1] with p（t）〉0,0〈q（t）〈b＊,t∈[0,1],b＊ is the first eigenvalue of the Robin problem （p（t）＇）＇＋bu=0,u＇（0）=0,u（1）=0 By applying the topological degree theory and global bifurcation techniques, we establish the existence results of positive solutions for above problem.
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