具有非局部Stieltjes积分边值条件半正(k,n-k)边值问题的非平凡解

Nontrivial Solutions of Semi-positone(k,n-k)Boundary Value Problem Subject to Nonlocal Boundary Conditions with Stieltjes Integrals

应用拓扑度方法证明了具有非局部Stieltjes积分边值条件半正(k,n-k)边值问题非平凡解的存在性,其中非线性项f可以不是非负的但下方有界.给出了正解存在性的两个推论,它们是非线性项f非负情形已有结论的推广.通过两个例子来说明主要结论,例子的混合边值条件包含变号系数的多点条件和变号核的积分条件.

The existence of nontrivial solutions is obtained by topological degree method for semi-positone(k,n-k) boundary value problem subject to nonlocal boundary conditions with Stieltjes integrals in which the nonlinearity f may not be nonnegative but bounded below.Two corollaries are given for the existence of positive solutions that are the extension of previous results when f is nonnegative.Two examples are presented to illustrate the main results that have mixed boundary conditions involving multi-point with sign-changing coefficients and integral with sign-changing kernel.