含有一阶导数的一维p-Laplacian算子方程的可解性

Solvability of One-dimensional p-Laplacian Operator Equation with First Derivative

应用Schauder不动点定理,研究含有一维p-Laplacian算子的非线性两点边值问题的可解性,得到这类方程的解的几个存在性定理,结果表明:如果非线性项在其定义域的某个有界子集上的"高度"是适当的,那么该问题必存在解或正解。

By applying Schauder fixed point theorem, we study the solvability of one--dimensional p--Laplacian operator equation for the nonlinear two--point boundary value problems with one--dimensional p--Laplacian operator and get some existence theorems . The main results show that the class of equations has at least, one solution or positive solution if the “height” of nonlinear term is appropriate on a bounded subset of its definitional domain.