具有p-Laplace算子的一类高阶奇异边值问题解的存在性

Existence of Solutions to a Class of Higher-Order Singular Boundary Value Problem for One-Dimensional $p$-Laplacian

中文关键词:  高阶奇异微分方程  正解  Vitali 收敛定理.

英文关键词:singular higher-order differential equation  positive solution  Vitali's convergence theorem.

中文摘要:

      本文研究下面问题的正解$$\left\{\begin{array}{ll} (\Phi_p(x^{(n-1)}(t)))'+f(t, \ldots, x^{(n-1)})=0,\,\,\,\, 01.$ $f$ 在点 $x^{(i)}=0, i=0, \ldots, n-2$ 可能是奇异的. 证明建立在 Leray-Schauder 拓扑度和 Vitali 收敛定理的基础上.

英文摘要:

      This paper deals with the existence of positive solutions for the problem $$\left\{\begin{array}{ll} (\Phi_p(x^{(n-1)}(t)))'+f(t, x, \ldots, x^{(n-1)})=0,\,\,\,\, 01.$ $f$ may be singular at $x^{(i)}=0, i=0, \ldots, n-2$. The proof is based on the Leray-Schauder degree and Vitali's convergence theorem.