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EXISTENCE AND UNIQUENESS FOR THIRD ORDER NONLINEAR BOUNDARY VALUE PROBLEMS 被引量:5
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作者 WANG GUOCAN Department of Basic Science, Dalian Institute of Railway Technology, Dalian 116022 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1996年第1期7-16,共10页
In this paper, the existence and uniqueness of solutions for boundary valueproblem x′′′=f(t, x, x′, x″), x(0)=A, x′(0)=B, g(x′(1), x″(1))=0 are studied byusing Volterra type operator and upper and lower soluti... In this paper, the existence and uniqueness of solutions for boundary valueproblem x′′′=f(t, x, x′, x″), x(0)=A, x′(0)=B, g(x′(1), x″(1))=0 are studied byusing Volterra type operator and upper and lower solutions. Our results improve someknown works. 展开更多
关键词 Third order nonlinear boundary value problem existence and uniqueness Volterra type operator upper and lower solutions.
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Singular Perturbations for a Class of Fourth-order Nonlinear Boundary Value Problem 被引量:2
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作者 LI Xu WANG Shi-peng 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第2期217-222,共6页
This paper is devoted to study the following the singularly perturbed fourth-order ordinary differential equation ∈y(4) =f(t,y',y'',y'''),0t1,0ε1 with the nonlinear boundary conditions y(0)=y'(1)=0,p... This paper is devoted to study the following the singularly perturbed fourth-order ordinary differential equation ∈y(4) =f(t,y',y'',y'''),0t1,0ε1 with the nonlinear boundary conditions y(0)=y'(1)=0,p(y''(0),y'''(0))=0,q(y''(1),y'''(1))=0 where f:[0,1]×R3→R is continuous,p,q:R2→R are continuous.Under certain conditions,by introducing an appropriate stretching transformation and constructing boundary layer corrective terms,an asymptotic expansion for the solution of the problem is obtained.And then the uniformly validity of solution is proved by using the differential inequalities. 展开更多
关键词 singular perturbation nonlinear boundary value problem differential inequality asymptotic expansion
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THE NONLINEAR BOUNDARY VALUE PROBLEM FOR A CLASS OF INTEGRO-DIFFERENTIAL SYSTEM 被引量:1
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作者 Rongrong Tang 《Analysis in Theory and Applications》 2006年第3期254-261,共8页
In this paper, using the theory of differential inequalities, we study the nonlinear boundary value problem for a class of integro-differential system. Under appropriate assumptions, the existence of solution is prove... In this paper, using the theory of differential inequalities, we study the nonlinear boundary value problem for a class of integro-differential system. Under appropriate assumptions, the existence of solution is proved and the uniformly valid asymptotic expansions for arbitrary n-th order approximation and the estimation of remainder term are obtained simply and conveniently. 展开更多
关键词 integro-differential system nonlinear boundary value problem differential inequality
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ON THE EXISTENCE AND NODAL CHARACTER OF SOLUTIONS OF SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS 被引量:1
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作者 曹道珉 邓引斌 《Acta Mathematica Scientia》 SCIE CSCD 1990年第4期471-478,共8页
In this paper we prove the existence of k-node solution of singular nonlinear boundary value problems for each k is-an-element-of N union {0}.
关键词 ON THE EXISTENCE AND NODAL CHARACTER OF SOLUTIONS OF SINGULAR nonlinear boundary value PROBLEMS BVP
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ON THE EXISTENCE AND NODAL CHARACTER OF THE SOLUTIONS OF SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS 被引量:1
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作者 曹道珉 邓引斌 《Acta Mathematica Scientia》 SCIE CSCD 1991年第4期443-461,共19页
1. Introduction We consider the singular nonlinear boundary value problem where l=v+3/v-1,l+1 is the critical exponent of the embedding of weighted Sobolev space Wt21,2(O, +∞) into Lt2q(O, ∞), v>2. When v=N-1... 1. Introduction We consider the singular nonlinear boundary value problem where l=v+3/v-1,l+1 is the critical exponent of the embedding of weighted Sobolev space Wt21,2(O, +∞) into Lt2q(O, ∞), v>2. When v=N-1 we can get the radial solutions of problem where 2*=2N/N-2 is the critical exponent of the Sobolev embedding H1(Rn)→LQ(RN). Kurtz has discussed the existence of κ-node solution of (1.1), (1.2) for each κ∈N U{0} when the growth rate of |u|l-1u+f(u) is lower then |u|v+3/v-1 i.e. 展开更多
关键词 ON THE EXISTENCE AND NODAL CHARACTER OF THE SOLUTIONS OF SINGULAR nonlinear boundary value PROBLEMS
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Nonlinear boundary value problems for discontinuous delayed differential equations
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作者 SUN Wu-jun Department of Finance & Insurance, Business School of Nanjing University, Nanjing 210093, China 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2010年第1期9-17,共9页
In this paper nonlinear boundary value problems for discontinuous delayed differen- tial equations are considered. Some existence and boundedness results of solutions are obtained via the method of upper and lower sol... In this paper nonlinear boundary value problems for discontinuous delayed differen- tial equations are considered. Some existence and boundedness results of solutions are obtained via the method of upper and lower solutions, which may be discontinuous. Our analysis can be applied to those phenomena from physics and control theory which have been successfully described by delayed differential equations with discontinuous functions, such as electric, pneu- matic, and hydraulic networks. It is also an important step to precede the design of control signals when finite-time or practical stability control are concerned. 展开更多
关键词 nonlinear boundary value problems upper and lower solutions discontinuous delayed differentialequations Carath^odory conditions existence of solutions.
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EXISTENCE OF THREE-SOLUTIONS FOR SECOND-ORDER DIFFERENTIAL EQUATIONS WITH NONLINEAR BOUNDARY VALUE CONDITIONS
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作者 Liu BinDept.ofMath.,HuazhongUniv.ofScienceandTechnology,Wuhan430074,China.CollegeofMath.andStatist.,WuhanUniv.,Wuhan430072,China 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2002年第2期135-144,共10页
The paper deals with the existence of three- solutions for the second- order differential equations with nonlinear boundary value conditions x″=f(t,x,x′) , t∈ [a,b], g1(x(a) ,x′(a) ) =0 , g2 (x(b) ,x′(... The paper deals with the existence of three- solutions for the second- order differential equations with nonlinear boundary value conditions x″=f(t,x,x′) , t∈ [a,b], g1(x(a) ,x′(a) ) =0 , g2 (x(b) ,x′(b) ) =0 , where f :[a,b]× R1× R1→ R1,gi:R1× R1→ R1(i=1 ,2 ) are continuous functions.The methods employed are the coincidence degree theory.As an application,the sufficient conditions under which there are arbitrary odd solutions for the BVP are obtained 展开更多
关键词 coincidence degree three- solutions theorem nonlinear boundary value conditions
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THE SINGULARLY PERTURBED NONLINEAR BOUNDARY VALUE PROBLEMS 被引量:8
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作者 Mo JiaqiDept.of Math.,Anhui Normal Univ.,Wuhu 241000. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2000年第4期377-382,共6页
The singularly perturbed nonlinear boundary value problems are considered.Using the stretched variable and the method of boundary layer correction,the formal asymptotic expansion of solution is obtained.And then the u... The singularly perturbed nonlinear boundary value problems are considered.Using the stretched variable and the method of boundary layer correction,the formal asymptotic expansion of solution is obtained.And then the uniform validity of solution is proved by using the differential inequalities. 展开更多
关键词 Singular perturbation nonlinear boundary value problem differential inequality asymptotic expansion.
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Newton-EGMSOR Methods for Solution of Second Order Two-Point Nonlinear Boundary Value Problems
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作者 Jumat Sulaiman Mohd Khatim Hasan +1 位作者 Mohamed Othman Samsul Ariffin Abdul Karim 《Journal of Mathematics and System Science》 2012年第3期185-190,共6页
The convergence results of block iterative schemes from the EG (Explicit Group) family have been shown to be one of efficient iterative methods in solving any linear systems generated from approximation equations. A... The convergence results of block iterative schemes from the EG (Explicit Group) family have been shown to be one of efficient iterative methods in solving any linear systems generated from approximation equations. Apart from block iterative methods, the formulation of the MSOR (Modified Successive Over-Relaxation) method known as SOR method with red-black ordering strategy by using two accelerated parameters, ω and ω′, has also improved the convergence rate of the standard SOR method. Due to the effectiveness of these iterative methods, the primary goal of this paper is to examine the performance of the EG family without or with accelerated parameters in solving second order two-point nonlinear boundary value problems. In this work, the second order two-point nonlinear boundary value problems need to be discretized by using the second order central difference scheme in constructing a nonlinear finite difference approximation equation. Then this approximation equation leads to a nonlinear system. As well known that to linearize nonlinear systems, the Newton method has been proposed to transform the original system into the form of linear system. In addition to that, the basic formulation and implementation of 2 and 4-point EG iterative methods based on GS (Gauss-Seidel), SOR and MSOR approaches, namely EGGS, EGSOR and EGMSOR respectively are also presented. Then, combinations between the EG family and Newton scheme are indicated as EGGS-Newton, EGSOR-Newton and EGMSOR-Newton methods respectively. For comparison purpose, several numerical experiments of three problems are conducted in examining the effectiveness of tested methods. Finally, it can be concluded that the 4-point EGMSOR-Newton method is more superior in accelerating the convergence rate compared with the tested methods. 展开更多
关键词 Explicit group MSOR iteration second order scheme two-point nonlinear boundary value problem.
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THE EXISTENCE OF SOLUTIONS OF NONLINEAR BOUNDARY VALUE PROBLEMS INVOLVING THE p-LAPLACIAN OPERATOR IN L^s-SPACES 被引量:17
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作者 WEI Li (School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China Institute of Applied Mathematics and Mechanics, Ordnance Engineering College, Shijiazhuang 050003, China. ZHOU Haiyun (Institute of Applied Mathematics and Mechanics, Ordnance Engineering College, Shijiazhuang 050003, China Institute of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016, China. 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2005年第4期511-521,共11页
By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we study the abstract results on the existence of a solution u ∈ L^s (Ω) of nonlinear boundary value probl... By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we study the abstract results on the existence of a solution u ∈ L^s (Ω) of nonlinear boundary value problems involving the p-Laplacian operator, where 2≤ s〈+∞, and 2N/N+1 〈 p ≤ 2 for N(≥ 1) which denotes the dimension of R^N. To obtain the result, some new techniques are used in this paper. The equation discussed in this paper and our methods here are extension and complement to the corresponding results of L. Wei and Z. He. 展开更多
关键词 Maximal monotone operator accretive mapping hemi-continuous mapping p-Laplacian operator nonlinear boundary value problem.
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A sixth-order wavelet integral collocation method for solving nonlinear boundary value problems in three dimensions 被引量:1
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作者 Zhichun Hou Jiong Weng +2 位作者 Xiaojing Liu Youhe Zhou Jizeng Wang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2022年第2期81-92,I0003,共13页
A sixth-order accurate wavelet integral collocation method is proposed for solving high-order nonlinear boundary value problems in three dimensions.In order to realize the establishment of this method,an approximate e... A sixth-order accurate wavelet integral collocation method is proposed for solving high-order nonlinear boundary value problems in three dimensions.In order to realize the establishment of this method,an approximate expression of multiple integrals of a continuous function defined in a three-dimensional bounded domain is proposed by combining wavelet expansion and Lagrange boundary extension.Through applying such an integral technique,during the solution of nonlinear partial differential equations,the unknown function and its lower-order partial derivatives can be approximately expressed by its highest-order partial derivative values at nodes.A set of nonlinear algebraic equations with respect to these nodal values of the highest-order partial derivative is obtained using a collocation method.The validation and convergence of the proposed method are examined through several benchmark problems,including the eighth-order two-dimensional and fourth-order three-dimensional boundary value problems and the large deflection bending of von Karman plates.Results demonstrate that the present method has higher accuracy and convergence rate than most existing numerical methods.Most importantly,the convergence rate of the proposed method seems to be independent of the order of the differential equations,because it is always sixth order for second-,fourth-,sixth-,and even eighth-order problems. 展开更多
关键词 nonlinear boundary value problems Eighth-order derivative Coiflet wavelet Integral collocation method Von Karman plate
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SOME NEW RESULTS FOR NONLINEAR BOUNDARY VALUE PROBLEMS OF MIXED TYPE INTEGRODIFFERENTIAL EQUATION 被引量:1
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作者 王国灿 金丽 《Annals of Differential Equations》 2003年第2期202-208,共7页
In this paper we give the existence and uniqueness of solutions for boundary value problems of the form u' = f(t, u,u', T1u,T2u), g(u(0),u(1)) = 0, h(w(0), u(1),u'(0), u'(1)) = 0 by means of the upper ... In this paper we give the existence and uniqueness of solutions for boundary value problems of the form u' = f(t, u,u', T1u,T2u), g(u(0),u(1)) = 0, h(w(0), u(1),u'(0), u'(1)) = 0 by means of the upper and lower solution method. 展开更多
关键词 nonlinear boundary value problems upper and lower solutions existence and uniqueness mixed type integrodifferential equation
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NONLINEAR BOUNDARY VALUE PROBLEMS FOR FIRST ORDER DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENTS 被引量:1
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作者 张凤琴 马知恩 《Annals of Differential Equations》 2003年第3期431-438,共8页
The authors employ the method of upper and lower solutions coupled with the monotone iterative technique to obtain some results of existence and un-iqueness for nonlinear boundary value problem of differential equatio... The authors employ the method of upper and lower solutions coupled with the monotone iterative technique to obtain some results of existence and un-iqueness for nonlinear boundary value problem of differential equations with piecewise constant arguments. 展开更多
关键词 nonlinear boundary value problem monotone iterative technique lower and upper related solutions differential equations with piecewise constant arguments
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SINGULAR PERTURBATION FOR A NONLINEAR BOUNDARY VALUE PROBLEM OF FIRST ORDER SYSTEM
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作者 陈松林 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1996年第11期1095-1100,共6页
In this paper, we study the following perturbed nonlinear boundary value problemof the form:εx' =f(t, x,y, ε)εy' =g(t, x,y, ε)x(0)= A(ξ1,ξ2 ,x(1) -x(0), y(1 )- y(0), ε)y(0)=B(ξ1, ξ2,x(1)- ̄x(0 ),y(1 )... In this paper, we study the following perturbed nonlinear boundary value problemof the form:εx' =f(t, x,y, ε)εy' =g(t, x,y, ε)x(0)= A(ξ1,ξ2 ,x(1) -x(0), y(1 )- y(0), ε)y(0)=B(ξ1, ξ2,x(1)- ̄x(0 ),y(1 )-g(0 ),ε)where ξ1, ξ2 are functions of ε. 0<ε<<1. Under some suitable conditions, we give the asymptotic expansion of solution of any order, and obtain the estimation of remaindet term by using the comparison theorem. 展开更多
关键词 nonlinear boundary value singular perturbation comparisontheorem asymptotic expansion
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SINGULAR PERTURBATIONS FOR A CLASS OF BOUNDARY VALUE PROBLEMS OF HIGHER ORDER NONLINEAR DIFFERENTIAL EQUATIONS
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作者 史玉明 刘光旭 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1996年第12期1193-1201,共9页
In this paper, it has been studied that the singular perturbations for the higherorder nonlinear boundary value problem of the formε2y(n)=f(t, ε, y. '', y(n-2))pj(ε)y(1)(0, ε)-qj(ε)y(j+1)(0. ε)=Aj(ε) (0... In this paper, it has been studied that the singular perturbations for the higherorder nonlinear boundary value problem of the formε2y(n)=f(t, ε, y. '', y(n-2))pj(ε)y(1)(0, ε)-qj(ε)y(j+1)(0. ε)=Aj(ε) (0≤j≤n-3)a1(ε)u(n-2)(0.ε)-a2(ε)y(n-1)(0, ε)=B(ε)b1(ε)y(n-2)(1, ε)+b2(ε)y(n-1),(1. ε)=C(ε)by the method of higher order differential inequalities and boundary layer corrections.Under some mild conditions, the existence of the perturbed solution is proved and itsuniformly efficient asymptotic expansions up to its n-th order derivative function aregiven out. Hence, the existing results are extended and improved. 展开更多
关键词 nonlinear boundary value problem singular perturbation uniformly efficient asymptotic expansion higher orderdifferential inequalities boundary layer correction
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Non-E_2 Class of Strongly Nonlinear Generalised R-H Boundary Value Problems for Second-Order Elliptic System
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作者 Li Mingzhong Xu Dinghua (College of Sciences) 《Advances in Manufacturing》 SCIE CAS 1998年第3期3-11,共9页
In this paper, a class of strongly non linear generalised Riemann Hilbert problems for second order elliptic system is studied. By means of the theory of integral equations and using an explicit form of the solutio... In this paper, a class of strongly non linear generalised Riemann Hilbert problems for second order elliptic system is studied. By means of the theory of integral equations and using an explicit form of the solution, a reduction is made to a nonlinear boundary value problem for two holomorphic functions. And using an approximation dealing with a solvable perturbed problems and suitable prior estimates, we prove that the problems possess solution in Hardy class, the solution w(z) belongs to W 1 2()∩W 2 p(G),p>2 . 展开更多
关键词 nonlinear boundary value problems perturbed method priori estimation existence theorem
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EXISTENCE AND UNIQUENESS FOR SECOND-ORDER VECTOR BOUNDARY VALUE PROBLEM OF NONLINEAR SYSTEMS
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作者 Du Zengji Lin Xiaojie Ge Weigao 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2005年第3期323-330,共8页
This paper is concerned with the following second-order vector boundary value problem :x^R=f(t,Sx,x,x'),0〈t〈1,x(0)=A,g(x(1),x'(1))=B,where x,f,g,A and B are n-vectors. Under appropriate assumptions,exis... This paper is concerned with the following second-order vector boundary value problem :x^R=f(t,Sx,x,x'),0〈t〈1,x(0)=A,g(x(1),x'(1))=B,where x,f,g,A and B are n-vectors. Under appropriate assumptions,existence and uniqueness of solutions are obtained by using upper and lower solutions method. 展开更多
关键词 vector differential equation nonlinear boundary value problem existence and uniqueness upper and lower solutions method.
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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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A simultaneous space-time wavelet method for nonlinear initial boundary value problems 被引量:1
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作者 Jizeng WANG Lei ZHANG Youhe ZHOU 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2018年第11期1547-1566,共20页
A high-precision and space-time fully decoupled numerical method is developed for a class of nonlinear initial boundary value problems. It is established based on a proposed Coiflet-based approximation scheme with an ... A high-precision and space-time fully decoupled numerical method is developed for a class of nonlinear initial boundary value problems. It is established based on a proposed Coiflet-based approximation scheme with an adjustable high order for the functions over a bounded interval, which allows the expansion coefficients to be explicitly expressed by the function values at a series of single points. When the solution method is used, the nonlinear initial boundary value problems are first spatially discretized into a series of nonlinear initial value problems by combining the proposed wavelet approximation and the conventional Galerkin method, and a novel high-order step-by-step time integrating approach is then developed for the resulting nonlinear initial value problems with the same function approximation scheme based on the wavelet theory. The solution method is shown to have the N th-order accuracy, as long as the Coiflet with [0, 3 N-1]compact support is adopted, where N can be any positive even number. Typical examples in mechanics are considered to justify the accuracy and efficiency of the method. 展开更多
关键词 nonlinear initial boundary value problem Coiflet numerical method
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PERIODIC BOUNDARY VALUE PROBLEMS FOR NONLINEAR IMPULSIVEINTEGRODIFFERENTIAL EQUATIONS OF MIXED TYPE IN BANACH SPACES 被引量:1
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作者 韦忠礼 《Acta Mathematica Scientia》 SCIE CSCD 1997年第1期35-43,共9页
In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by me... In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by means of the monotone iterative technique and cone theory based on a comparison result. 展开更多
关键词 CE PN EPC PERIODIC boundary value PROBLEMS FOR nonlinear IMPULSIVEINTEGRODIFFERENTIAL EQUATIONS OF MIXED TYPE IN BANACH SPACES EI
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