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The Estimation for Lower Bounds of the Solutions of Fermat's Equation
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作者 乐茂华 《Chinese Quarterly Journal of Mathematics》 CSCD 1992年第2期52-55,共4页
Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|x... Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|xyz, x<y<z, then y>p^(6p-2)/2. 展开更多
关键词 Fermat's last theorem integer solution lower bound
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A PRIORI ESTIMATE FOR LOWER SOLUTIONS OF ACLASS QUASILINEAR ELLIPTIC EQUATIONS 被引量:1
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作者 王向东 韩普宪 梁■廷 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第2期231-232,共2页
A new priori estimate of lower- solution is made for the following quasilinear elliptic equation : integral(G) {del v . A (x, u, del u) + vB (x, u, del u)} dx = 0, For All v is an element of (W) over circle(p)(1) (G).... A new priori estimate of lower- solution is made for the following quasilinear elliptic equation : integral(G) {del v . A (x, u, del u) + vB (x, u, del u)} dx = 0, For All v is an element of (W) over circle(p)(1) (G). The result presented in this paper enriches and extends the corresponding result of Gilbarg-Trudinger. 展开更多
关键词 elliptic equation lower solution priori estimate
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A Generalized Upper and Lower Solution Method for Singular Discrete Boundary Value Problems 被引量:1
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作者 胡卫敏 韦俊 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2007年第2期212-219,共8页
This paper presents new existence results for singular discrete boundary value problems. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign.
关键词 upper and lower solutions discrete boundary value problem EXISTENCE SINGULAR
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Upper and Lower Semicontinuity of Solution Sets for Parametric Generalized Vector Quasi-equilibrium Problems
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作者 LI AI-QIN FAN LI-YA 《Communications in Mathematical Research》 CSCD 2011年第1期1-5,共5页
In this paper, two kinds of parametric generalized vector quasi-equilibrium problems are introduced and the relations between them are studied. The upper and lower semicontinuity of their solution sets to parameters a... In this paper, two kinds of parametric generalized vector quasi-equilibrium problems are introduced and the relations between them are studied. The upper and lower semicontinuity of their solution sets to parameters are investigated. 展开更多
关键词 parametric generalized vector quasi-equilibrium problem solution set upper semicontinuity lower semicontinuity set-valued mapping
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Upper and Lower Solutions for Impulsive Differential Equations with Application to ODE
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作者 綦建刚 王克宁 《Northeastern Mathematical Journal》 CSCD 2002年第3期189-196,共8页
In this paper, we establish the existence of upper and lower solutions for a periodic boundary value problems (PBVP for short) of impulsive differential equations. which guarantees the existence of at least one soluti... In this paper, we establish the existence of upper and lower solutions for a periodic boundary value problems (PBVP for short) of impulsive differential equations. which guarantees the existence of at least one solution for the problem. As an application, these results are applied to PBVP of ODE and some examples are given to illustrate our results. 展开更多
关键词 impulsive differential equatin upper and lower solution periodic boundary value problem
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On the Measurement of Lower Solution Bounds of the Discrete Algebraic Lyapunov Equation
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作者 Chien-Hua Lee 《Journal of Applied Mathematics and Physics》 2016年第4期655-661,共7页
In this paper, estimations of the lower solution bounds for the discrete algebraic Lyapunov Equation (the DALE) are addressed. By utilizing linear algebraic techniques, several new lower solution bounds of the DALE ar... In this paper, estimations of the lower solution bounds for the discrete algebraic Lyapunov Equation (the DALE) are addressed. By utilizing linear algebraic techniques, several new lower solution bounds of the DALE are presented. We also propose numerical algorithms to develop sharper solution bounds. The obtained bounds can give a supplement to those appeared in the literature.  展开更多
关键词 Discrete Lyapunov Equation Estimation lower solution Bound Linear Algebraic Technique
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Existence of Solutions for S-L Singular Boundary Value Problems with p-Laplacian Operators
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作者 郭彦平 葛渭高 单文锐 《Journal of Beijing Institute of Technology》 EI CAS 2002年第2期220-224,共5页
The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solution... The existence of solutions for singular nonlinear two point boundary value problems subject to Sturm Liouville boundary conditions with p Laplacian operators is studied by the method of upper and lower solutions. The proof is based on an application of Schauder’s fixed point theorem to a modified problem whose solutions are that of the original one. At the same time, Arzela Ascoli theorem is used to prove that the defined operator N is a compact map. 展开更多
关键词 nonlinear boundary value problems p Laplacian operators fixed point upper solution lower solution
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Existence of Positive Solutions for a Class of Degenerate and Nondegenerate Stable Diffusion Models
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作者 张彦肖 《Chinese Quarterly Journal of Mathematics》 CSCD 2000年第3期50-56,共7页
This paper is concerned with a class of degenerate and nondegenerate stable diffusion models.By using the upper and lower solution method and Schauder fixed point principle,the author studies the existence of positive... This paper is concerned with a class of degenerate and nondegenerate stable diffusion models.By using the upper and lower solution method and Schauder fixed point principle,the author studies the existence of positive solutions for these stable_diffusion models under some conditions. 展开更多
关键词 weak upper and lower solutions elliptic system positive solution
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NEW EXISTENCE RESULTS OF POSITIVE SOLUTION FOR A CLASS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS 被引量:4
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作者 李楠 王长有 《Acta Mathematica Scientia》 SCIE CSCD 2013年第3期847-854,共8页
In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term witho... In this article, the existence and uniqueness of positive solution for a class of nonlinear fractional differential equations is proved by constructing the upper and lower control functions of the nonlinear term without any monotone requirement. Our main method to the problem is the method of upper and lower solutions and Schauder fixed point theorem. Finally, we give an example to illuminate our results. 展开更多
关键词 Fractional differential equations positive solution upper and lower solutions existence and uniqueness fixed point theorem
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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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SOME NECESSARY AND SUFFICIENT CONDITIONS FOR EXISTENCE OF POSITIVE SOLUTIONS FOR THIRD ORDER SINGULAR SUBLINEAR MULTI-POINT BOUNDARY VALUE PROBLEMS 被引量:5
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作者 韦忠礼 《Acta Mathematica Scientia》 SCIE CSCD 2014年第6期1795-1810,共16页
We mainly study the existence of positive solutions for the following third order singular multi-point boundary value problem{x^(3)(t) + f(t, x(t), x′(t)) = 0, 0 〈 t 〈 1,x(0)-∑i=1^m1 αi x(ξi) = 0... We mainly study the existence of positive solutions for the following third order singular multi-point boundary value problem{x^(3)(t) + f(t, x(t), x′(t)) = 0, 0 〈 t 〈 1,x(0)-∑i=1^m1 αi x(ξi) = 0, x′(0)-∑i=1^m2 βi x′(ηi) = 0, x′(1)=0,where 0 ≤ ai≤∑i=1^m1 αi 〈 1, i = 1, 2, ···, m1, 0 〈 ξ1〈 ξ2〈 ··· 〈 ξm1〈 1, 0 ≤βj≤∑i^m2=1βi〈1,J=1,2, ···, m2, 0 〈 η1〈 η2〈 ··· 〈 ηm2〈 1. And we obtain some necessa βi 〈=11, j = 1,ry and sufficient conditions for the existence of C^1[0, 1] and C^2[0, 1] positive solutions by constructing lower and upper solutions and by using the comparison theorem. Our nonlinearity f(t, x, y)may be singular at x, y, t = 0 and/or t = 1. 展开更多
关键词 boundary value problems positive solutions lower and upper solutions comparison theorem
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ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE HEAT EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS 被引量:1
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作者 汤燕斌 周笠 Omer Ali 《Acta Mathematica Scientia》 SCIE CSCD 2004年第2期307-312,共6页
The purpose of this paper is to investigate the stability and asymptotic behavior of the time-dependent solutions to a linear parabolic equation with nonlinear boundary condition in relation to their corresponding ste... The purpose of this paper is to investigate the stability and asymptotic behavior of the time-dependent solutions to a linear parabolic equation with nonlinear boundary condition in relation to their corresponding steady state solutions. Then, the above results are extended to a semilinear parabolic equation with nonlinear boundary condition by analyzing the corresponding eigenvalue problem and using the method of upper and lower solutions. 展开更多
关键词 Asymptotic behavior heat equation nonlinear boundary condition upper and lower solutions
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Existence of Multiple Positive Solutions of Discrete Boundary Value Problem
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作者 周桂云 《Chinese Quarterly Journal of Mathematics》 CSCD 2002年第4期99-104,共6页
In this paper, we consider the existence of multiple positive solutions of discrete boundary value problem. The theory of fixed point index is used here to derive the existence theorem.
关键词 nonlinear difference equation upper and lower solutions the fixed point index
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A class of singular perturbation solutions to semilinear equations of fourth order
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作者 莫嘉琪 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第11期1455-1460,共6页
A class of singularly perturbed boundary value problems for semilinear equations of fourth order with two parameters are considered. Under suitable conditions, using the method of lower and upper solutions, the existe... A class of singularly perturbed boundary value problems for semilinear equations of fourth order with two parameters are considered. Under suitable conditions, using the method of lower and upper solutions, the existence and the asymptotic behavior of the solution to the boundary value problem are studied, In the present paper, the solution to the original singularly perturbed problem with two parameters has only one boundary layer. 展开更多
关键词 NONLINEAR two parameters singular perturbation lower and upper solutions
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ASYMPTOTIC SOLUTION OF SINGULARLY PERTURBED PROBLEM FOR A NONLINEAR SINGULAR EQUATION
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作者 MoJiaqi LinWantao 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2004年第2期187-190,共4页
The singularly perturbed initial value problem for a nonlinear singular equation is considered. By using a simple and special method the asymptotic behavior of solution is studied.
关键词 NONLINEAR singular equation singular perturbation upper and lower solutions.
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Existence of Positive Solutions for A Fourth-order Boundary Value Problems with p-Laplacian Operators
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作者 WANG Wan-peng 《Chinese Quarterly Journal of Mathematics》 2018年第4期377-385,共9页
This paper investigates the existence of positive solutions for a fourth-order p-Laplacian nonlinear equation. We show that, under suitable conditions, there exists a positive number λ~*such that the above problem ha... This paper investigates the existence of positive solutions for a fourth-order p-Laplacian nonlinear equation. We show that, under suitable conditions, there exists a positive number λ~*such that the above problem has at least two positive solutions for 0 < λ < λ~* , at least one positive solution for λ = λ~* and no solution forλ > λ~* by using the upper and lower solutions method and fixed point theory. 展开更多
关键词 FOURTH-ORDER P-LAPLACIAN POSITIVE solutionS UPPER and lower solutionS method Fixed point theory
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The Existence and Uniqueness of Positive Solutions for a Singular Nonlinear Three-Point Boundary Value Problems
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作者 Yao Dong Baoqiang Yan 《Journal of Applied Mathematics and Physics》 2018年第12期2600-2620,共21页
Using the method of lower and upper solutions, we study the following singular nonlinear three-point boundary value problems: , where K ∈ C[0,1] ,0 α η < 1 and λ is a positive parameter and present the existenc... Using the method of lower and upper solutions, we study the following singular nonlinear three-point boundary value problems: , where K ∈ C[0,1] ,0 α η < 1 and λ is a positive parameter and present the existence, uniqueness, and the dependency on parameters of the positive solutions under various assumptions. Our result improves those in the previous literatures. 展开更多
关键词 Three-Point Boundary Value Problem Positive solution lower and UPPER solutions EIGENVALUE and EIGENFUNCTION
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Existence of Solutions for Boundary Value Problems of Conformable Fractional Differential Equations
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作者 Xingyue Jian 《Journal of Applied Mathematics and Physics》 2019年第1期233-242,共10页
In this paper, we study a class of boundary value problems for conformable fractional differential equations under a new definition. Firstly, by using the monotone iterative technique and the method of coupled upper a... In this paper, we study a class of boundary value problems for conformable fractional differential equations under a new definition. Firstly, by using the monotone iterative technique and the method of coupled upper and lower solution, the sufficient condition for the existence of the boundary value problem is obtained, and the range of the solution is determined. Then the existence and uniqueness of the solution are proved by the proof by contradiction. Finally, a concrete example is given to illustrate the wide applicability of our main results. 展开更多
关键词 Boundary Value Problems Conformable Fractional Differential Equations The Method of COUPLED UPPER and lower solution COUPLED solution MONOTONE ITERATION
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Existence of Solutions to the Higher Order Nonlinear Differential Equations
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作者 TANG Lin-shan JIANG Cheng-shun 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第1期1-10,共10页
This paper is concerned with the following n-th ordinary differential equation:{u~(n)(t)=f(t,u(t),u~(1)(t),···,u~(n-1) (t)),for t∈(0,1),u~(i) (0)=0,0 ≤i≤n3,au~(n-2)(0)du~(n-1)(0)=0,cu~(n-2)(1)... This paper is concerned with the following n-th ordinary differential equation:{u~(n)(t)=f(t,u(t),u~(1)(t),···,u~(n-1) (t)),for t∈(0,1),u~(i) (0)=0,0 ≤i≤n3,au~(n-2)(0)du~(n-1)(0)=0,cu~(n-2)(1)+du~(n-1)(1)=0,where a,c ∈ R,,≥,such that a~2 + b~2 >0 and c~2+d~2>0,n ≥ 2,f:[0,1] × R → R is a continuous function.Assume that f satisfies one-sided Nagumo condition,the existence theorems of solutions of the boundary value problem for the n-th-order nonlinear differential equations above are established by using Leray-Schauder degree theory,lower and upper solutions,a priori estimate technique. 展开更多
关键词 n-th order boundary value problems one-sided Nagumo condition lower and upper solutions a priori estimates Leray-Schauder degree
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Existence of Non-trivial Nonnegative Periodic Solutions for a Nonlinear Diffusion System
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作者 孙杰宝 金春花 柯媛元 《Northeastern Mathematical Journal》 CSCD 2007年第2期167-175,共9页
In this paper, by the method of upper and lower solutions, we establish the existence of the non-trivial nonnegative periodic solutions for a class of degenerate diffusion system arising from dynamics of biological gr... In this paper, by the method of upper and lower solutions, we establish the existence of the non-trivial nonnegative periodic solutions for a class of degenerate diffusion system arising from dynamics of biological groups. 展开更多
关键词 periodic solution nonlinear diffusion system upper and lower solution
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