含有一阶导数的一维p-Laplace方程的正解(英文)

Positive Solution to an One-Dimensional p-Laplacian with First Derivative

通过利用积分方程全连续算子的不动点指数对含有一阶导数的一维p-L ap lace方程建立了一个存在定理.这个定理表明此p-L ap lace方程必有一个正解,只要非线性项在某个有界集合上的“最大高度”是适当的.

By applying the integral equations and the fixed point index of completely continuous operators an existenee theorem is established for an one-dimensional p-Laplacian with first derivative. This theorem shows that the p-Laplacian can have one positive solution provided the ＂maximal height＂ of nonlinear term is appropriate on a bounded set.