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-  2018 

一类非线性二阶常微分方程 Dirichlet问题正解的存在性
Existence of positive solutions for a class of nonlinear second-order Dirichlet problem

DOI: 10.6040/j.issn.1671-9352.0.2017.178

Keywords: Green 函数,正解,Dirichlet 问题,存在性,
Green function
,existence,positive solutions,Dirichlet problem

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摘要: 运用锥上的不动点定理研究了一类带 Dirichlet 边界条件的二阶边值问题{u″(t)+a(t)u(t)+f(t,u(t))=0, t∈(0,1),u(0)=u(1)=0正解的存在性, 其中 a∈C([0,1], [0,∞))且在(0,1)的任意子区间内 a(t)?0, f∈C([0,1]×[0,∞), [0,∞))。所得结果推广和改进了已有工作的相关结果。
Abstract: The existence of positive solutions for a class of second-order Dirichlet problem{u″(t)+a(t)u(t)+f(t,u(t))=0, t∈(0,1),u(0)=u(1)=0is studied by using the fixed-point theorem in cones, where a∈C([0,1], [0,∞))and a(t)?0 on any subinterval of(0,1), f∈C([0,1]×[0,∞), [0,∞)). The results generalize and improve the related results of the existingwork


[1]  ALKHUTOV Y, BORSUK M. The Dirichlet problem in a cone for second-order elliptic quasi-linear equation with the <i>p</i>-Laplacian[J]. Journal of Mathematical Analysis and Applications, 2017, 449(2):1351-1367.
[2]  WAN Haitao. The second-order expansion of solutions to a singular Dirichlet boundary value problem[J]. Journal of Mathematical Analysis and Applications, 2015, 427(1):140-170.
[3]  DUMANYAN V Z. On the solvability of the Dirichlet problem for a second-order elliptic equation[J]. Doklady. Natsional'naya Akademiya Nauk Armenii, 2014, 114(4):295-308.
[4]  徐登州, 马如云. 线性微分方程的非线性扰动[M]. 北京: 科学出版社, 2008:214-218. XU Dengzhou, MA Ruyun. Nonlinear disturbance of linear differential equation[M]. Beijing: Science Press, 2008:214-218.
[5]  马如云. 非线性常微分方程非局部问题[M]. 北京: 科学出版社, 2004:18-20. MA Ruyun. Nonlocal problem of nonlinear ordinary differential equation[M]. Beijing: Science Press, 2004:18-20.
[6]  EFENDIEV B I. The Dirichlet problem for an ordinary continuous second-order differential equation[J]. Matematicheskie Zametki, 2018, 103(2):295-302.
[7]  ZHAO Jin, WANG Yanchao. Nontrivial solutions of second-order singular Dirichlet systems[J]. Boundary Value Problems, 2017, 180(14):34-15.
[8]  WANG Hanyan. On the existence of positive solutions for semilinear elliptic equations in the annulus[J]. Journal of Differential Equations, 1994, 109(1):1-7.
[9]  LI Yongxiang. Positive solutions of second-order boundary value problems with sign-changing nonlinear terms[J]. Journal of Mathematical Analysis and Applications, 2003, 282(1):232-240.
[10]  GRITSANS A, SADYRBAEV F, YERMACHENKO I. Dirichlet boundary value problem for the second-order asymptotically linear system[J]. International Journal of Differential Equations, 2016, 35(5):1-12.


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