| 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 |
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| 引用本文： | 尹晨阳,马跃萧,张国伟.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[J].应用数学学报,2020(1):62-78. |
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| 作者姓名： | 尹晨阳 马跃萧 张国伟 |
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| 作者单位： | 东北大学数学系 |
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| 基金项目： | 国家自然科学基金(61473065);国家级大学生创新创业训练计划(201810145026)资助项目 |
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| 摘 要： | 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.
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| 关 键 词： | 非平凡解 正解 拓扑度 |
Nontrivial Solutions of Semi-positone(k,n-k)Boundary Value Problem Subject to Nonlocal Boundary Conditions with Stieltjes Integrals |
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| YIN Chenyang,MA Yuexiao,ZHANG Guowei.Nontrivial Solutions of Semi-positone(k,n-k)Boundary Value Problem Subject to Nonlocal Boundary Conditions with Stieltjes Integrals[J].Acta Mathematicae Applicatae Sinica,2020(1):62-78. |
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| Authors: | YIN Chenyang MA Yuexiao ZHANG Guowei |
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| Institution: | (Department of Mathematics,Northeastern University,Shenyang 110819,China) |
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| Abstract: | 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. |
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| Keywords: | nontrivial solution positive solution topological degree |
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