一维p-Laplace方程Robin问题的正解

Positive Solutions of the Robin Problem for One-Dimensional p-Laplacian Equations

主要研究如下一维p-Laplace方程Robin问题的正解的存在性:-((u′)p-1)′=f(t,u),u(0)=u′(1)=0,其中p>1,f∈C([0,1]×+,+).在借助于Jensen不等式获得先验估计的基础上,运用不动点指数理论,证明了以上问题1个正解和多重正解存在性的几个结果.最后,把主要结果应用于建立一维p-Laplace方程Dirichlet问题1个对称正解和多重对称正解的存在性.

This paper is mainly concerned with the existence and multiplicity of positive solutions to the Robin problem for the one-dimensional p-Laplacian equation{-（（u′）p-1）′=f（t,u）, u（0）=u′（1）=0,where p 1,f∈C（×R＋,R＋）.Based on a priori estimates achieved by utilizing Jensen＇s inequality,we use the fixed point index theory to prove our main results of existence and multiplicity of positive solutions to the above problem.Finally,our main results are applied to establish some results of symmetric positive solutions to the Dirichlet problem for one-dimensional p-Laplacian equations.