非局部 Sturm-Liouville 型边值条件下四阶方程的正解

Positive Solutions of Fourth-Order Equations under Nonlocal Boundary Value Conditions of Sturm-Liouville Type

中文关键词:  正解  不动点指数  锥

英文关键词:positive solution  fixed point index  cone

中文摘要:

      在本文中我们研究带Stieltjes积分的非局部Sturm-Liouville型边值条件下四阶问题, 其非线性项含有一阶和二阶导数. 利用在一个特殊锥上的不动点指数方法, 对于非线性项提出了一些不等式条件, 它们保证了该问题正解的存在性.给出了在具有变号系数多点和变号核积分的混合边值条件下几个例子来支持主要结论.

英文摘要:

      In this paper, we study the fourth-order problem with the first and second derivatives in nonlinearity under nonlocal boundary value conditions of Sturm-Liouville type involving Stieltjes integrals. Some inequality conditions on nonlinearity are presented that guarantee the existence of positive solutions to the problem by the theory of fixed point index on a special cone. Some examples are provided to support the main results under mixed boundary conditions containing multi-point with sign-changing coefficients and integral with sign-changing kernel.