障碍带条件下p-Laplacian方程两点边值问题的可解性

Solvability of Two-Point Problems for p-Laplacian Equation under Barrier Strips Conditions

摘要: 本文运用Leray-Schauder原理研究障碍带条件下p-Laplacian方程两点边值问题$\{\begin{array}{l}{\left(\phi \left(u^{\prime }\right)\right)}^{\prime }=f\left(t,u\left(t\right),u^{\prime }\left(t\right)\right),t\in \left[0,1\right],\hfill \\ u\left(0\right)=A,u^{\prime }\left(1\right)=B,\hfill \end{array}$ 解的存在性，其中${\phi }_p\left(s\right)={\left|s\right|}^{p-2}s$ ，$s\in ℝ$ ，$p>1$ ，非线性项$f:\left[0,1\right]\times {ℝ}^2\to ℝ$ 连续。

Abstract: In this paper, by using Leray-Schauder theory, the existence of solutions to the following p-Laplacian equation two-point problem under the barrier strips conditions$\{\begin{array}{l}{\left(\phi \left(u^{\prime }\right)\right)}^{\prime }=f\left(t,u\left(t\right),u^{\prime }\left(t\right)\right),t\in \left[0,1\right],\hfill \\ u\left(0\right)=A,u^{\prime }\left(1\right)=B,\hfill \end{array}$ is considered, where ${\phi }_p\left(s\right)={\left|s\right|}^{p-2}s$ , $s\in ℝ$ , $p>1$ , $f:\left[0,1\right]\times {ℝ}^2\to ℝ$ is continuous.