带双井势函数的一维p-Laplace方程解对应层的位置

The locatin of the layers of the solution to a class of one-dimensional p-Laplace equation with double well potential

研究了一类带双井势函数的一维p-Laplace方程解,主要讨论了方程解对应层的位置情况.解的零点与交换层是一一对应的,得出方程解对应的层出现在h(x)的局部极值点附近.在h(x)的局部极小值点附近只可能出现一个交换层,而多层出现在h(x)的局部极大值点附近.

The problem of the location of the layers of the solution to a class of one-dimensional p-Laplace equation with double well potential was put forward.There is an one-one correspondence between the zeros and the layers of the solutions.The layers only appear near the local extreme points of h（x）.At most a single layer can appear near each local minimum point of h（x）,the multi-layers can appear near the local maximum point of h（x）.