中文摘要：

研究了二阶Neumann边值问题{u″＋f（t,u,u＇）=s,t∈（0,1）,u＇（0）=u＇（1）=0解的个数与参数s的关系,其中f∈C（[0,1]×R2,R）,s∈R。运用上下解方法及拓扑度理论,获得存在常数s1∈R,当ss1时,该问题至少有两个解。

英文摘要：

We study the relationship between s and the number of solutions of the second-order Neumann boundary value problem{u″ ＋ f（ t,u,u＇） = s,t∈（ 0,1）,u＇（ 0） = u＇（ 1） = 0,where f∈C（ [0,1]× R2,R）,s∈R is a parameter. By using the method of the upper and lower solutions and topological degree techniques,we obtain that the problem has no solution,at least one solution and at least two solutions,when s s1,s = s1,s s1,respectively.