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The problem on the existence of a positive in the interval ]a, b[ solution of the boundary value problem
is considered, where the functions f and
satisfy the local Carathéodory conditions. The possibility for the functions f and g to have singularities in the first argument (for t = a and t = b) and in the phase variable (for u = 0) is not excluded. Sufficient and, in some cases, necessary and sufficient conditions for the solvability of that problem are established. 相似文献
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利用上下解方法及单调迭代技术讨论了一类非线性分数阶微分方程的奇异边值问题,给出了其解的存在及最小最大解的存在定理. 相似文献
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Shu-hongWu 《应用数学学报(英文版)》2005,21(1):77-80
A two-point boundary value problem with a non-negative parameter Q arising in the study of surface tension induced flow of a liquid metal or semiconductor is studied. We prove that the problem has at least one solution for Q≥0.This improves a recent result that the problem has at least one solution for 0 ≤Q≤13.21. 相似文献
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By constructing suitable Banach space.an existence theorem is established under a condition of linear growth for the third-order boundary value problem u'"(t) f(t,u(t),t'(t),u"(t))=0,0<t<1,u(0)=u'(0)=u'(1)=0,where the nonlinear term contains first and second derivatives of unknown function.In this theorem the nonlinear term f(t,u,v,w)may be singular at t=0 and t=1.The main ingredient is Leray-Schauder nonlinear alternative. 相似文献
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考察了二阶常微分方程u″(t)+f(t,u(t))+h(t)=0,a.e.t∈[0,1]在Sturm-Liouville边值条件下的正解,其中f(t,u)是非负弱Caratheodory函数并且允许h(t)■0.利用锥拉伸与锥压缩型的Krasnoselskii不动点定理,建立了有限或无穷多个正解的存在性.、 相似文献
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系数变号时经典Emden方程的两点边值问题的正解 总被引:3,自引:0,他引:3
姚庆六 《应用泛函分析学报》2001,3(2):107-111
建立了边值问题w″ k(t)w^α=0,w(0)=w(1)=0的一个正解存在定理,其中允许k(t)的[0,1]上改变符号。 相似文献
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主要考虑如下三阶两点边值问题通过对非线性项f作适当的限制,利用上下解方法,获得三阶两点边值问题解的存在性结果.特别之处是,一个截断技巧和Nagumo条件的引入和使用.同时得到了解的唯一性结果. 相似文献
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In this paper, we consider the following singular nonlinear problem
where A is a positive continuous function on (0,1), q is a nonnegative measurable function on [0,1] and f is a nonnegative regular function on (0,1)×(0,).We suppose that
0
1
dt/A(t)< and 0<
0
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A(t)q(t) dt<. Then we prove the existence and the uniqueness of a positive solution of this problem (P).Our approach is based on the use of the Green's function and the Schauder's fixed point theorem. 相似文献
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利用重合度理论研究了一类具偏差变元的Duffing型方程x″ f(x(t))x′ g(t,x(t-τ(t)))=p(t).获得了该方程存在ω-周期解的若干新结论,改进和推广了已有文献中的相关结果. 相似文献
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HUANG Wen-hua LU Chuan 《数学季刊》2007,22(3):451-458
In this paper, a mini max theorem was showed mega which the paper proves a new existent and unique result on solution of the boundary value problem for the nonlinear wave equation by using the mini max theorem. 相似文献
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Solutions to Boundary Value Problem of Nonlinear Impulsive Differential Equation of Fractional Order
This paper is devoted to study the existence and uniqueness of solutions to a boundary value problem of nonlinear fractional differential equation with impulsive effects.The arguments are based upon Schauder and Banach fixed-point theorems. We improve and generalize the results presented in[B.Ahmad,S.Sivasundaram, Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations,Nonlinear Analysis:Hybrid Systems,3(2009),251- 258]. 相似文献
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首先利用微分不等式理论和一些分析技巧,探讨了一类具非线性边界条件的二阶Volterra型泛函微分方程边值问题解的存在性问题.然后通过对右端边界层函数和外部解的构造,进一步研究了一类具小参数的二阶Votterra型非线性边值问题.利用微分中值定理和上、下解方法得到了边值问题解的存在性,并给出了解的关于小参数的一致有效渐近展开式. 相似文献
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