具有凸-凹-凸非线性项的边值问题正解的确切个数

doi:10.12677/AAM.2017.63037

期刊菜单

具有凸-凹-凸非线性项的边值问题正解的确切个数
Exact Multiplicity of Positive Solutions for Convex-Concave-Convex Nonlinearities

DOI: 10.12677/AAM.2017.63037, PDF, HTML, XML, 下载: 1,550 浏览: 2,241
作者: 黄子饶, 白定勇：广州大学数学与信息科学学院，广东广州
关键词: 确切正解个数；狄利克雷边值问题；分支曲线；时间映射；Exact Multiplicity of Positive Solutions； Dirichlet Boundary Value Problem； Bifurcation Curve； Time-Map

摘要: 本文研究了具有凸-凹-凸非线性项的狄利克雷边值问题正解的分支曲线。通过时间映射分析法，证明了在非线性项为渐近次线性时，边值问题的正解分支曲线为S-型曲线，从而确定了边值问题的正解的确切个数。

Abstract: In this paper we study the bifurcation curve of the Dirichlet boundary value problem with convex- concave-convex nonlinearities. By using Time-map techniques, we prove that the bifurcation curve of the boundary value problem is S-shaped when the nonlinearities are asymptotic sublinear. Consequently, the exact multiplicity of positive solutions is determined.

文章引用：黄子饶, 白定勇. 具有凸-凹-凸非线性项的边值问题正解的确切个数[J]. 应用数学进展, 2017, 6(3): 317-326. https://doi.org/10.12677/AAM.2017.63037

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