p-Laplace算子方程非齐次边值问题的上下解方法

Method of lower and upper solutions for non-homogeneous boundary value problems of type p-Laplacian equation

研究了一类具p-Laplace算子的二阶非线性常微分方程在非齐次边界条件下的两点边值问题.通过变换,将具p-Laplace算子的二阶微分方程边值问题转化为一阶常微分方程边值问题,利用上下解方法,在较弱的条件下得到了最大解和最小解的存在性定理.

By using the upper and lower solutions method, the existence of solutions was studied for a type of second-order two-points boundary value problems with p-Laplacian operator under non-homogeneous boundary conditions. By means of the transformation the second-order two-points boundary value problems with p-Laplacian operator were changed into the first-order two-points boundary value problems, and the suffcient conditions of the existence of maximum solution and minimum solution were obtained under the weaker conditions.