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争鸣     
问题  问题61 笔者在教学中,遇到了这样一个有趣的问题,同学们给出了三种不同的解法,都认为自己的解法有道理.然后,我们几个老师在一起讨论,也有所分歧.现请贵刊予以讨论.题目 设函数y=F(x) ,其定义域为[0 ,+∞) ,值域为R,已知F(x2 - 2 mx+ m+ 2 )的值域为R,求m的取值范围.解法1 令f(x) =x2 - 2 mx+ m+ 2 ,则可转化为对任意x∈R,f(x)≥0恒成立.故Δ=4 m2 - 4(m+ 2 )≤0 ,∴- 1≤m≤2 .解法2 由题意,y=f(x)的图象与直线y=0相切,即f(x)的最小值为0 (x∈R) .故Δ=4 m2 - 4(m+ 2 ) =0 ,∴m=- 1或m=2 .解法3 由题意,只要保证f(x)能取遍…  相似文献   
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In this paper, we investigate the existence of positive solutions for singular fourthorder integral boundary-value problem with p-Laplacian operator by using the upper and lower solution method and fixed point theorem. Nonlinear term may be singular at t= 0 and/or t - 1 and x =0.  相似文献   
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The existence of positive solutions to a boundary value problem of second-order impulsive singular integro-differential equation with integral boundary conditions in a Banach space is obtained by means of fixed point theory.Moreover,an application is also given to illustrate the main result.  相似文献   
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In this paper, the cone theory and MSnch fixed point theorem combined with the monotone iterative technique are used to investigate the positive solutions for a class of systems of nonlinear singular differential equations with multi-point boundary value conditions on the half line in a Banach space. The conditions for the existence of positive solutions are formulated. In addition, an explicit iterative approximation of the solution is also derived.  相似文献   
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