一维p-laplace方程解的存在性

利用时间-映射结合Leray—Shauder度的方法对一维p-laplace方程混合边值问题进行了研究。通过建立Leray-Shauder度引理，提出了一维p-laplace方程混合边值问题正解的存在性定理，并且证明了该定理的正确性。

The existence of solutions of the one-dimensional p-laplace equation with mixed boundary value problem

The Dirichlet problem of the one-dimensional p-laplace was studied extensively. Many scholars have proved the existence of the solution, the weak solution and the positive solution of the Dirichlet problem. But there is a little research about the one-dimensional p-laplace with the mixed boundary value problem. Using the method of time-mapping and Leray-Shauder degree to study the existence of solutions of the one-dimensional p-Laplace with the mixed boundary value condition was studied. From the lemma of Leray-Shauder degree the existence theory of the positive solution was put foward. The result indicated that the theory is correct.