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Existence Results of Third Order Multi-Point Boundary Value Problem at Resonance 被引量:3
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作者 杜增吉 白占兵 葛渭高 《Journal of Beijing Institute of Technology》 EI CAS 2005年第4期449-452,共4页
A kind of third order multi-point boundary value problems, x'''( ι) = f( t, x ( t ), x" ( t ), x''' ( t ) ) + m 2 e(t),t∈(0, 1),x(0)=ax(ξ),x'(0)-0,x(l)= ^m2∑j=1 βjx(ηj), fεC[0,... A kind of third order multi-point boundary value problems, x'''( ι) = f( t, x ( t ), x" ( t ), x''' ( t ) ) + m 2 e(t),t∈(0, 1),x(0)=ax(ξ),x'(0)-0,x(l)= ^m2∑j=1 βjx(ηj), fεC[0, 1]×R^3, e(t)∈L^1[0, 1],a≥0, is considered, all theβj's have not the same sign, 0〈ξ〈 l, 0〈η1〈 η2〈… 〈ηm.2〈 1. By using the coincidence degree theory, some existence theorems for the problems at resonance are obtained. 展开更多
关键词 multi-point boundary value problem RESONANCE coincidence degree theory
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SOLUTIONS TO A SECOND-ORDER MULTI-POINT BOUNDARY VALUE PROBLEM AT RESONANCE 被引量:2
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作者 杜增吉 孟凡超 《Acta Mathematica Scientia》 SCIE CSCD 2010年第5期1567-1576,共10页
This article deals with the following second-order multi-point boundary value problem x″(t)=r(t,x(t),x′(t))+e(t),t∈(0,1)x′(0)=m∑i=1aix′(ξi),x(1)=n∑j=1βjx(ηj), Under the resonance conditi... This article deals with the following second-order multi-point boundary value problem x″(t)=r(t,x(t),x′(t))+e(t),t∈(0,1)x′(0)=m∑i=1aix′(ξi),x(1)=n∑j=1βjx(ηj), Under the resonance conditions m∑i=1ai=1,n∑j=1βj=1,n∑j=1βjηj=1 , by applying the coincidence degree theory, some existence results of the problem are established. The emphasis here is that the dimension of the linear operator is two. In this paper, we extend and improve some previously known results like the ones in the references. 展开更多
关键词 coincidence degree multi-point boundary value problem RESONANCE
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Multi-point Boundary Value Problems for Nonlinear Fourth-order Differential Equations with All Order Derivatives
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作者 Yang Liu Shi Shao-yun 《Communications in Mathematical Research》 CSCD 2013年第2期108-120,共13页
By using fixed point theorem, multiple positive solutions for some fourth- order multi-point boundary value problems with nonlinearity depending on all order derivatives are obtained. The associated Green's functions... By using fixed point theorem, multiple positive solutions for some fourth- order multi-point boundary value problems with nonlinearity depending on all order derivatives are obtained. The associated Green's functions are also given. 展开更多
关键词 multi-point boundary value problem positive solution CONE fixed point
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EXISTENCE OF SOLUTIONS FOR HIGHER ORDER MULTI-POINT BOUNDARY VALUE PROBLEM AT RESONANCE 被引量:3
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作者 林晓洁 杜增吉 葛渭高 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第5期705-711,共7页
Using the theory of coincidence degree, a class of higher order multi-point boundary value problem for ordinary differential equations are studied. Under the boundary conditions satisfying the resonance case, some new... Using the theory of coincidence degree, a class of higher order multi-point boundary value problem for ordinary differential equations are studied. Under the boundary conditions satisfying the resonance case, some new existence results are obtained by supposing some conditions to the nonlinear term and applying a priori estimates. 展开更多
关键词 boundary value problem RESONANCE coincidence degree theory
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Existence and Uniqueness of Solutions for Higher Order Nonlinear Multi-point Boundary Value Problems 被引量:7
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作者 PEI Ming-he Sung-Kag Chang 《Chinese Quarterly Journal of Mathematics》 CSCD 2009年第2期258-266,共9页
In this paper, the existence and uniqueness theorems of solutions of k-point boundary value problems for nth-order nonlinear differential equations are established by Leray-Schauder continuation theorem.
关键词 nth-order nonlinear differential equations k-point boundary value problem EXISTENCE UNIQUENESS
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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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Existence of Positive Solutions for a Third-Order Multi-Point Boundary Value Problem 被引量:2
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作者 A. Guezane-Lakoud L. Zenkoufi 《Applied Mathematics》 2012年第9期1008-1013,共6页
By using Leray-Schauder nonlinear alternative, Banach contraction theorem and Guo-Krasnosel’skii theorem, we discuss the existence, uniqueness and positivity of solution to the third-order multi-point nonhomogeneous ... By using Leray-Schauder nonlinear alternative, Banach contraction theorem and Guo-Krasnosel’skii theorem, we discuss the existence, uniqueness and positivity of solution to the third-order multi-point nonhomogeneous boundary value problem (BVP1): where for The interesting point lies in the fact that the nonlinear term is allowed to depend on the first order derivative . 展开更多
关键词 Guo’s Fixed POINT THEOREM Three POINT boundary value problem Positive Solution LERAY SCHAUDER Non-Linear Alternative CONTRACTION Principle
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Positive Solutions for Fractional Differential Equations with Multi-Point Boundary Value Problems 被引量:1
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作者 Lina Zhou Weihua Jiang 《Journal of Applied Mathematics and Physics》 2014年第5期108-114,共7页
In this paper, a fractional multi-point boundary value problem is considered. By using the fixed point index theory and Krein-Rutman theorem, some results on existence are obtained.
关键词 Caputo FRACTIONAL DERIVATIVE FRACTIONAL INTEGRAL boundary value problem Fixed Point Index Theory
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Existence of Solution to Multi-Point Boundary Value Problems at Resonance
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作者 薛春艳 高晶 葛渭高 《Journal of Beijing Institute of Technology》 EI CAS 2005年第2期203-207,共5页
A class of second order multi-point boundary value problem at resonance is considered. Under some appropriate conditions, the existence of solutions to the nonlinear problem is obtained by use of the coincidence degre... A class of second order multi-point boundary value problem at resonance is considered. Under some appropriate conditions, the existence of solutions to the nonlinear problem is obtained by use of the coincidence degree theory of Mawhin. 展开更多
关键词 boundary value problem (BVP) Fredholm operator RESONANCE
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A Compact Difference Scheme for Multi-point Boundary Value Problems of Heat Equations
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作者 Xuping Wang Zhizhong Sun 《Communications on Applied Mathematics and Computation》 2019年第4期545-563,共19页
In this paper,a compact difference scheme is established for the heat equations with multi-point boundary value conditions.The truncation error of the difference scheme is O(τ2+h^4),where t and h are the temporal ste... In this paper,a compact difference scheme is established for the heat equations with multi-point boundary value conditions.The truncation error of the difference scheme is O(τ2+h^4),where t and h are the temporal step size and the spatial step size.A prior estimate of the difference solution in a weighted norm is obtained.The unique solvability,stability and convergence of the difference scheme are proved by the energy method.The theoretical statements for the solution of the difference scheme are supported by numerical examples. 展开更多
关键词 Heat EQUATION - multi-point boundary value CONDITION COMPACT DIFFERENCE scheme Energy method
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Existence of Solutions for a Multi-point Boundary Value Problems with Three Dimension Kernal at Resonance
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作者 LIANG Ju-hua REN Li-shun ZHAO Zhi-liang 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第1期138-143,共6页
In this paper,a multi-point boundary value problems for a three order nonlinear deferential equation is considered.With the help of coincidence theorem due to Mawhin,a existence theorem is obtained.
关键词 boundary value problems coincidence degree theorem existence theorem 2000 MR Subject Classification:34B10 34B15
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The Existence of Solutions for a Third-Orde, r Multi-Point Boundary Value Problem at Resonance
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作者 Weihua Jiang Jiqing Qiu Ruiyan Li 《数学计算(中英文版)》 2013年第2期13-18,共6页
关键词 共振问题 多点边值问题 解的存在性 BANACH空间 重合度理论 运营商 边界值 三阶
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Dirac method for nonlinear and non-homogenous boundary value problems of plates
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作者 Xiaoye MAO Jiabin WU +2 位作者 Junning ZHANG Hu DING Liqun CHEN 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2024年第1期15-38,共24页
The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundar... The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundary value problem of rectangular plates is proposed. The key concept behind this method is to transform the nonlinear or non-homogeneous part on the boundary into a lateral force within the governing function by the Dirac operator, which linearizes and homogenizes the original boundary, allowing one to employ the modal superposition method for obtaining solutions to reconstructive governing equations. Once projected into the modal space, the harmonic balance method(HBM) is utilized to solve coupled ordinary differential equations(ODEs)of truncated systems with nonlinearity. To validate the convergence and accuracy of the proposed Dirac method, the results of typical examples, involving nonlinearly restricted boundaries, moment excitation, and displacement excitation, are compared with those of the differential quadrature element method(DQEM). The results demonstrate that when dealing with nonlinear boundaries, the Dirac method exhibits more excellent accuracy and convergence compared with the DQEM. However, when facing displacement excitation, there exist some discrepancies between the proposed approach and simulations;nevertheless, the proposed method still accurately predicts resonant frequencies while being uniquely capable of handling nonuniform displacement excitations. Overall, this methodology offers a convenient way for addressing nonlinear and non-homogenous plate boundaries. 展开更多
关键词 rectangular plate Dirac operator nonlinear boundary time-dependent boundary boundary value problem
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CAUCHY TYPE INTEGRALS AND A BOUNDARY VALUE PROBLEM IN A COMPLEX CLIFFORD ANALYSIS
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作者 曹南斌 李尊凤 +1 位作者 杨贺菊 乔玉英 《Acta Mathematica Scientia》 SCIE CSCD 2024年第1期369-385,共17页
Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quan... Clifford analysis is an important branch of modern analysis;it has a very important theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the H?lder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution. 展开更多
关键词 Clifford analysis Cauchy type integral Plemelj formula Holder continuous boundary value problems
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Wavelet Multi-Resolution Interpolation Galerkin Method for Linear Singularly Perturbed Boundary Value Problems
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作者 Jiaqun Wang Guanxu Pan +1 位作者 Youhe Zhou Xiaojing Liu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第4期297-318,共22页
In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be r... In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin node.Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients.All the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element method.Four numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet method.The results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary layer.Compared with many other methods,the proposed method possesses satisfactory accuracy and efficiency.The theoretical and numerical results demonstrate that the order of theε-uniform convergence of this wavelet method can reach 5. 展开更多
关键词 Wavelet multi-resolution interpolation Galerkin singularly perturbed boundary value problems mesh-free method Shishkin node boundary layer
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The Regularity of Solutions to Mixed Boundary Value Problems of Second-Order Elliptic Equations with Small Angles
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作者 Mingyu Wu 《Journal of Applied Mathematics and Physics》 2024年第4期1043-1049,共7页
This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of suff... This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order. 展开更多
关键词 Mixed boundary value problems for Elliptic Equations Small-Angle boundary value problems Regularity of Solutions to Elliptic Equations
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A Radial Basis Function Method with Improved Accuracy for Fourth Order Boundary Value Problems
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作者 Scott A. Sarra Derek Musgrave +1 位作者 Marcus Stone Joseph I. Powell 《Journal of Applied Mathematics and Physics》 2024年第7期2559-2573,共15页
Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with... Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with Radial Basis Function methods. The method is used to solve fourth order boundary value problems. The use and location of ghost points are examined in order to enforce the extra boundary conditions that are necessary to make a fourth-order problem well posed. The use of ghost points versus solving an overdetermined linear system via least squares is studied. For a general fourth-order boundary value problem, the recommended approach is to either use one of two novel sets of ghost centers introduced here or else to use a least squares approach. When using either ghost centers or least squares, the random variable shape parameter strategy results in significantly better accuracy than when a constant shape parameter is used. 展开更多
关键词 Numerical Partial Differential Equations boundary value problems Radial Basis Function Methods Ghost Points Variable Shape Parameter Least Squares
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THE NONLINEAR BOUNDARY VALUE PROBLEM FOR k HOLOMORPHIC FUNCTIONS IN C^(2)
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作者 崔艳艳 李尊凤 +1 位作者 谢永红 乔玉英 《Acta Mathematica Scientia》 SCIE CSCD 2023年第4期1571-1586,共16页
k holomorphic functions are a type of generation of holomorphic functions.In this paper,a nonlinear boundary value problem for k holomorphic functions is primarily discussed on generalized polycylinders in C^(2).The e... k holomorphic functions are a type of generation of holomorphic functions.In this paper,a nonlinear boundary value problem for k holomorphic functions is primarily discussed on generalized polycylinders in C^(2).The existence of the solution for the problem is studied in detail with the help of the boundary properties of Cauchy type singular integral operators with a k holomorphic kernel.Furthermore,the integral representation for the solution is obtained. 展开更多
关键词 k holomorphic functions boundary value problems Cauchy type singular integral operators
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Solvability of Multi-Point Boundary Value Problem
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作者 张慧星 刘文斌 +1 位作者 张建军 陈太勇 《Journal of Mathematical Research and Exposition》 CSCD 2009年第4期693-699,共7页
This paper deals with the existence of solutions for the problem{(Фp(u′))′=f(t,u,u′),t∈(0,1), u′(0)=0,u(1)=∑i=1^n-2aiu(ηi),where Фp(s)=|s|^p-2s,p〉1.0〈η1〈η2〈…〈ηn-2〈1,ai(i=1,2,…,n-... This paper deals with the existence of solutions for the problem{(Фp(u′))′=f(t,u,u′),t∈(0,1), u′(0)=0,u(1)=∑i=1^n-2aiu(ηi),where Фp(s)=|s|^p-2s,p〉1.0〈η1〈η2〈…〈ηn-2〈1,ai(i=1,2,…,n-2)are non-negative constants and ∑i=1^n-2ai=1.Some known results are improved under some sign and growth conditions. The proof is based on the Brouwer degree theory. 展开更多
关键词 p-Laplace multi-point boundary value problem RESONANCE degree theory.
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A Sparse Kernel Approximate Method for Fractional Boundary Value Problems
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作者 Hongfang Bai Ieng Tak Leong 《Communications on Applied Mathematics and Computation》 EI 2023年第4期1406-1421,共16页
In this paper,the weak pre-orthogonal adaptive Fourier decomposition(W-POAFD)method is applied to solve fractional boundary value problems(FBVPs)in the reproducing kernel Hilbert spaces(RKHSs)W_(0)^(4)[0,1] and W^(1)[... In this paper,the weak pre-orthogonal adaptive Fourier decomposition(W-POAFD)method is applied to solve fractional boundary value problems(FBVPs)in the reproducing kernel Hilbert spaces(RKHSs)W_(0)^(4)[0,1] and W^(1)[0,1].The process of the W-POAFD is as follows:(i)choose a dictionary and implement the pre-orthogonalization to all the dictionary elements;(ii)select points in[0,1]by the weak maximal selection principle to determine the corresponding orthonormalized dictionary elements iteratively;(iii)express the analytical solution as a linear combination of these determined dictionary elements.Convergence properties of numerical solutions are also discussed.The numerical experiments are carried out to illustrate the accuracy and efficiency of W-POAFD for solving FBVPs. 展开更多
关键词 Weak pre-orthogonal adaptive Fourier decomposition(W-POAFD) Weak maximal selection principle Fractional boundary value problems(FBVPs) Reproducing kernel Hilbert space(RKHS)
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