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POSITIVE SOLUTIONS FOR SINGULAR BVPs ON THE POSITIVE HALF-LINE ARISING FROM EPIDEMIOLOGY AND COMBUSTION THEORY 被引量:2
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作者 Smaïl Djebali Ouiza Saïfi 闫宝强 《Acta Mathematica Scientia》 SCIE CSCD 2012年第2期672-694,共23页
In this work, we are concerned with the existence and multiplicity of positive solutions for singular boundary value problems on the half-line. Two problems from epi- demiology and combustion theory set on the positiv... In this work, we are concerned with the existence and multiplicity of positive solutions for singular boundary value problems on the half-line. Two problems from epi- demiology and combustion theory set on the positive half-line are investigated upper and lower solution techniques combined with fixed point index on cones in priate Banach spaces. The results complement recent ones in the literature. We use appropriate Banach spaces. The results complement recent ones in the literature. 展开更多
关键词 Fixed points index positive solution singular problem cone lower andupper solution HALF-LINE
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POSITIVE SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER SINGULAR NONLINEAR DIFFERENTIAL EQUATIONS 被引量:2
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作者 LI Ren-gui(李仁贵) +1 位作者 LI Li-shan(刘立山) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第4期495-500,共6页
New existence results are presented for the singular second-order nonlinear boundary value problems u ' + g(t)f(u) = 0, 0 < t < 1, au(0) - betau ' (0) = 0, gammau(1) + deltau ' (1) = 0 under the cond... New existence results are presented for the singular second-order nonlinear boundary value problems u ' + g(t)f(u) = 0, 0 < t < 1, au(0) - betau ' (0) = 0, gammau(1) + deltau ' (1) = 0 under the conditions 0 less than or equal to f(0)(+) < M-1, m(1) < f(infinity)(-)less than or equal to infinity or 0 less than or equal to f(infinity)(+)< M-1, m(1) < f (-)(0)less than or equal to infinity where f(0)(+) = lim(u -->0)f(u)/u, f(infinity)(-)= lim(u --> infinity)f(u)/u, f(0)(-)= lim(u -->0)f(u)/u, f(infinity)(+) = lim(u --> infinity)f(u)/u, g may be singular at t = 0 and/or t = 1. The proof uses a fixed point theorem in cone theory. 展开更多
关键词 second-order singular boundary value problems positive solutions cone fixed point
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Positive Solution for a Singular Fourth-Order Differential System
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作者 B. Kovács 《Journal of Applied Mathematics and Physics》 2021年第9期2244-2257,共14页
In this paper, we investigate the existence of positive solutions for the singular fourth-order differential system <em>u</em><sup>(4)</sup> = <em><span style="white-space:nowrap;... In this paper, we investigate the existence of positive solutions for the singular fourth-order differential system <em>u</em><sup>(4)</sup> = <em><span style="white-space:nowrap;">φ</span>u</em> + <em>f </em>(<em>t</em>, <em>u</em>, <em>u</em>”, <em><span style="white-space:nowrap;">φ</span></em>), 0 < <em>t</em> < 1, -<em><span style="white-space:nowrap;">φ</span></em>” = <em>μg</em> (<em>t</em>, <em>u</em>, <em>u</em>”), 0 < <em>t</em> < 1, <em>u</em> (0) = <em>u</em> (1) = <em>u</em>”(0) = <em>u</em>”(1) = 0, <em><span style="white-space:nowrap;">φ</span> </em>(0) = <em><span style="white-space:nowrap;">φ</span> </em>(1) = 0;where <em>μ</em> > 0 is a constant, and the nonlinear terms<em> f</em>, <em>g</em> may be singular with respect to both the time and space variables. The results obtained herein generalize and improve some known results including singular and non-singular cases. 展开更多
关键词 positive solutions Fixed point Theorem singular solutions Bending of an Elastic Beam cone Boundary Value Problem Existence MULTIPLICITY
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Existence of Positive Solutions for Singular Second-order m-Point Boundary Value Problems 被引量:23
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作者 Guo-weiZhang Jing-xianSun 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2004年第4期655-664,共10页
The singular second-order m-point boundary value problem , is considered under some conditions concerning the first eigenvalue of the relevant linear operators, where (L&#981;)(x) = (p(x)&#981;&#8242... The singular second-order m-point boundary value problem , is considered under some conditions concerning the first eigenvalue of the relevant linear operators, where (L&#981;)(x) = (p(x)&#981;&#8242;(x))&#8242; + q(x)&#981;(x) and &#958;<SUB> i </SUB>&#8712; (0, 1) with 0 【 &#958;<SUB>1</SUB> 【 &#958;<SUB>2</SUB> 【 · · · 【 &#958;<SUB> m&#8722;2</SUB> 【 1, a <SUB>i </SUB>&#8712; [0, &#8734;). h(x) is allowed to be singular at x = 0 and x = 1. The existence of positive solutions is obtained by means of fixed point index theory. Similar conclusions hold for some other m-point boundary value conditions. 展开更多
关键词 Second-order singular equation multi-point boundary value problem positive solution cone fixed point index
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MULTIPLE POSITIVE SOLUTIONS OF A CLASS OF THREE-POINT SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS
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作者 Tian Yu Ge Weigao 《Annals of Differential Equations》 2005年第3期417-420,共4页
In this paper, the existence theorem for three positive solutions is presented for the singular nonlinear boundary value problem by applying the extended Five Functionals fixed point theorem.
关键词 singular nonlinear boundary value problem positive solutions cone fixed point theorem
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Positive Solutions of Singular Boundary Value Problems of Fourth-Order Differential Equations 被引量:3
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作者 CUI Yu Jun SUN Jing Xian ZOU Yu Mei 《Journal of Mathematical Research and Exposition》 CSCD 2009年第2期376-380,共5页
The singular boundary value problem{φ^(4)(x)-h(x)f(φ(x))=0,0〈x〈1, φ(0)=φ(1)=φ′(0)=φ′(1)=0.is considered under some conditions concerning the first eigenvaiues corresponding to the relevant ... The singular boundary value problem{φ^(4)(x)-h(x)f(φ(x))=0,0〈x〈1, φ(0)=φ(1)=φ′(0)=φ′(1)=0.is considered under some conditions concerning the first eigenvaiues corresponding to the relevant linear operators, where h(x) is allowed to be singular at both x = 0 and x = 1. The existence results of positive solutions are obtained by means of the cone theory and the fixed point index. 展开更多
关键词 singular boundary value problems positive solution cone fixed point index.
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MULTIPLE POSITIVE SOLUTIONS OF NONRESONANT SINGULAR BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS 被引量:3
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作者 韦忠礼 《Annals of Differential Equations》 2003年第2期209-219,共11页
This paper studies the existence of multiple positive solutions of nonresonant singular boundary value problem of second order ordinary differential equations. A sufficient condition for the existence of C[0,1] multip... This paper studies the existence of multiple positive solutions of nonresonant singular boundary value problem of second order ordinary differential equations. A sufficient condition for the existence of C[0,1] multiple positive solutions as well as C1[0, 1] multiple positive solutions is given by means of the fixed point theorems on cones. 展开更多
关键词 singular boundary value problem positive solution fixed point theorem cone NONRESONANCE
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POSITIVE SOLUTIONS OF NONLINEAR FOURTH-ORDER SINGULAR BOUNDARY VALUE PROBLEMS 被引量:1
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作者 Lü Haiyan Liu Yansheng 《Annals of Differential Equations》 2007年第3期288-296,共9页
By constructing a special cone and using the fixed point theorem of cone expansion and compression, this paper investigates fourth-order singular boundary value problems with sublinear effect and presents some necessa... By constructing a special cone and using the fixed point theorem of cone expansion and compression, this paper investigates fourth-order singular boundary value problems with sublinear effect and presents some necessary and sufficient conditions for existence of C2 or C3 positive solutions. Further, some examples are given concerning the applications of our main results. 展开更多
关键词 boundary value problem fixed point positive solution singularity cone
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ON THE EXISTENCE OF POSITIVE SOLUTIONS FOR SINGULAR NEUMANN BOUNDARY VALUE PROBLEMS
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作者 SunYan XuBenlong SunYongping 《Annals of Differential Equations》 2005年第2期203-208,共6页
By using fixed point index theory, we consider the existence of positive solutions for singular nonlinear Neumann boundary value problems. Our main results extend and improve many known results even for non-singular c... By using fixed point index theory, we consider the existence of positive solutions for singular nonlinear Neumann boundary value problems. Our main results extend and improve many known results even for non-singular cases. 展开更多
关键词 singular Neumann BVP positive solutions fixed point index theory cone EXISTENCE
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POSITIVE SOLUTIONS TO A CLASS OF SECOND-ORDER SINGULAR SEMIPOSITIVE NEUMANN BOUNDARY VALUE PROBLEM WITH GENERAL FORM
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作者 Zhilong Li (Dept. of Math., Jiangxi University of Finance and Economics, Nanchang 330013) 《Annals of Differential Equations》 2010年第3期284-291,共8页
By constructing an explicit Green function and using the fixed point index theory on a cone, we present some existence results of positive solutions to a class of second-order singular semipositive Neumann boundary va... By constructing an explicit Green function and using the fixed point index theory on a cone, we present some existence results of positive solutions to a class of second-order singular semipositive Neumann boundary value problem, where the nonlinear term is allowed to be nonnegative and unbounded. 展开更多
关键词 fixed point index theory singular Neumann boundary value problem positive solutions first positive eigenvalue
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EXISTENCE OF POSITIVE SOLUTIONS TO SINGULAR SUBLINEAR SEMIPOSITONE NEUMANN BOUNDARY VALUE PROBLEM
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作者 Zhilong Li,Shujun Jiang(Dept. of Math.,Jiangxi University of Finance and Economics,Nanchang 330013) 《Annals of Differential Equations》 2011年第3期336-342,共7页
The existence of positive solutions to a singular sublinear semipositone Neumann boundary value problem is considered. In this paper,the nonlinearity term is not necessary to be bounded from below and the function q(t... The existence of positive solutions to a singular sublinear semipositone Neumann boundary value problem is considered. In this paper,the nonlinearity term is not necessary to be bounded from below and the function q(t) is allowed to be singular at t = 0 and t = 1. 展开更多
关键词 positive solutions singular Neumann boundary value problem unbounded from below fixed point index theory
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二阶奇异非线性微分方程边值问题的正解 被引量:17
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作者 李仁贵 刘立山 《应用数学和力学》 EI CSCD 北大核心 2001年第4期435-440,共6页
分别在0≤f+0 <M1,m1<f- ∞ ≤∞和 0 ≤f+∞ <M1,m1<f- 0 ≤∞的情形下研究了非线性奇异边值问题u″+g(t)f(u) =0 ,0 <t <1,αu( 0 ) - βu′( 0 ) =0 ,γu( 1) +δu′( 1) =0 正解的存在性 ,其中f +0 =limu→ 0 f(u... 分别在0≤f+0 <M1,m1<f- ∞ ≤∞和 0 ≤f+∞ <M1,m1<f- 0 ≤∞的情形下研究了非线性奇异边值问题u″+g(t)f(u) =0 ,0 <t <1,αu( 0 ) - βu′( 0 ) =0 ,γu( 1) +δu′( 1) =0 正解的存在性 ,其中f +0 =limu→ 0 f(u) /u ,f- ∞ =limu→∞f(u) /u ,f- 0 =limu→ 0 f(u) /u ,f +∞=limu→∞f(u) /u ,g在区间 [0 。 展开更多
关键词 正解 不动点 二阶奇异非线性微分方程 边值问题 BANACH空间 Grean函数
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奇异非线性四阶边值问题的正解 被引量:5
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作者 孔令彬 张仲毅 《吉林大学学报(理学版)》 CAS CSCD 北大核心 2002年第1期40-43,共4页
证明存在两个正数 0 <λ <λ <+∞ ,使得奇异非线性四阶边值问题y( 4 ) (x) =λh(x)f(y(x) ) ,   0 <x <1 ,y( 0 ) =y( 1 ) =y′( 0 ) =y′( 1 ) =0 ,当λ∈ ( 0 ,λ )时 ,无正解 ;当λ∈ (λ ,+∞ )时 ,存在 1个正解 ... 证明存在两个正数 0 <λ <λ <+∞ ,使得奇异非线性四阶边值问题y( 4 ) (x) =λh(x)f(y(x) ) ,   0 <x <1 ,y( 0 ) =y( 1 ) =y′( 0 ) =y′( 1 ) =0 ,当λ∈ ( 0 ,λ )时 ,无正解 ;当λ∈ (λ ,+∞ )时 ,存在 1个正解 ;当λ∈ (λ ,+∞ )时 ,存在 3个解 ,其中有 2个为正解 ,只要f(y)在y =0处是超线性 ,并在y 展开更多
关键词 正解 不动点 奇异非线性四队边值问题 特征值 存在性 多解性
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一维p-Laplacian奇异Sturm-Liouville边值问题的正解 被引量:17
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作者 李翠哲 葛渭高 《应用数学》 CSCD 北大核心 2002年第3期13-17,共5页
本文在条件 0 ≤ f+ 0 <p(M1) ,p(m1) <f-∞ ≤∞或 0 ≤ f+ ∞ <p(M1) ,且p(m1) <f-0 ≤∞下 ,讨论奇异边值问题 (p(u′) )′+ g(t) f(u) =0 ,0 <t <1 ,au( 0 ) - βu′( 0 ) =0 ,γu( 1 ) +δu′( 1 ) =... 本文在条件 0 ≤ f+ 0 <p(M1) ,p(m1) <f-∞ ≤∞或 0 ≤ f+ ∞ <p(M1) ,且p(m1) <f-0 ≤∞下 ,讨论奇异边值问题 (p(u′) )′+ g(t) f(u) =0 ,0 <t <1 ,au( 0 ) - βu′( 0 ) =0 ,γu( 1 ) +δu′( 1 ) =0正解的存在性 ,其中p(u) =|u|p-2u ,p>1 ,f+ 0 =limu→ 0f(u)p(u) ,f-∞ =limu→∞f(u)p(u) ,f-0 =limu→ 0f(u)p(u) ,f+ ∞ =limu→∞f(u)p(u) ,g在区间 [0 ,1 ]的端点可以具有奇性 . 展开更多
关键词 奇异边值问题 锥上 不动点定理 P-LAPLACIAN算子 正解
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非线性分数阶微分方程组奇异对偶系统正解的存在性 被引量:5
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作者 张稳根 胡卫敏 刘刚 《四川师范大学学报(自然科学版)》 CAS CSCD 北大核心 2013年第6期887-892,共6页
分别应用锥上Leray-Schauder非线性抉择定理和Krasnoselskii’s不动点定理证明了非线性分数阶微分方程奇异对偶系统正解的存在性.
关键词 奇异 非线性分数阶微分方程 正解 锥不动点定理
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非线性奇异边值问题的正解 被引量:5
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作者 刘立山 孙彦 《数学物理学报(A辑)》 CSCD 北大核心 2005年第4期554-563,共10页
该文利用锥上的不动点定理,在较弱的条件下,讨论了非线性Sturm-Liouville方程奇异边值问题正解的存在性,并获得了当特征值λ在某一范围内取值时,边值问题至少存在一个正解的结论.作者的结果包含、推广并改进了许多已知的结果.
关键词 不动点理论 奇异边值问题 正解
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奇异二阶微分系统边值问题 被引量:3
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作者 白定勇 马如云 《中山大学学报(自然科学版)》 CAS CSCD 北大核心 2004年第2期129-132,共4页
运用锥拉伸与锥压缩原理,在适当的条件下建立一类奇异二阶微分系统边值问题正解的存在性。突破了有关文献中要求非线性项超线性或次线性增长的限制。
关键词 奇异边值问题 不动点 正解
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非线性奇异三阶两点边值问题单调正解的存在性 被引量:4
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作者 邹黄辉 王全义 《华侨大学学报(自然科学版)》 CAS 北大核心 2012年第6期699-704,共6页
利用锥压缩锥拉伸不动点定理及一些分析技巧,建立一类非线性奇异三阶两点边值问题存在一个及多个单调正解的充分条件,推广和改进了前人的研究成果.
关键词 单调正解 边值问题 不动点定理
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一类半正非线性多点边值问题多个正解的存在性 被引量:2
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作者 张新光 潘传中 《数学物理学报(A辑)》 CSCD 北大核心 2012年第5期996-1010,共15页
在适当的局部条件和超线性或次线性条件下,建立了一类具有半正非线性项的多点边值问题多个正解的存在性.扩充和提高了相关文献中两点和多点边值问题的许多结果,尤其是半正和正定的情况.
关键词 奇异边值问题 半正问题 正解 不动点
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二阶微分方程积分边值问题正解的存在性 被引量:3
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作者 陈东晓 陈应生 《华侨大学学报(自然科学版)》 CAS 北大核心 2013年第5期586-590,共5页
研究一类满足Sturm-Liouville积分边值条件的二阶非线性微分方程的正解存在性.通过转化为等价的积分方程,利用锥上不动点定理及一些分析技巧,建立边值问题存在一个和多个正解的充分条件.该边值条件含有勒贝格-斯梯阶积分,所得的结果是新的.
关键词 正解 边值问题 不动点理论 Sturm-Liouville积分
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