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一类四阶四点边值问题正解的存在性和多解性

, PP. 830-835

Keywords: 四阶四点边值问题,正解,存在性,特征值,不动点指数

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Abstract:

讨论了四阶四点边值问题u(4)(t)-g(t)f(t,u(t),u″(t))=0,t∈[0,1],u(0)=0,u(1)=0,au″(ξ1)-bu(ξ1)=0,cu″(ξ2)+du(ξ2)=0正解的存在性和多解性,其中,0≤ξ1≤ξ2≤1;a、b、c、d为非负常数;f[0,1]×[0,+∞)×(-∞,0][0,+∞)为Carathéodory函数;g∈L1[0,1].通过运用不动点指数理论,得到了一些正解存在的最优结果.

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