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Applied Mathematics and Mechanics(English Edition) 2000年第5期21卷 509-518页

作者：陈芳启陈予恕 Department of Mechanics Tianjin University 300072 Tianjin P R China

Using the monotone iterative method and Monch Fixed point theorem, the existence of solutions and coupled minimal and maximal quasisolutions of initial value problems for mixed monotone second-order integro-differential equations in Banach spaces are studied. Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained.

关键词： integro-differential equations Kuratowski measure of noncompactness coupled lower and upper quasisolutions monotone iterative method

monotone iterative methodfor Nonlinear Discontinuous ParabolicDifferential Equations

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Wuhan University Journal of Natural Sciences 1998年第4期3卷 389-393页

作者： Zou Qingsong Tian Yan Let Jingan(College of Mathematical Sciences, Wuhan University, Wuhan 430072, China) Wuhan University College of Mathematical Sciences Wuhan China (GRID:grid.49470.3e) (ISNI:***)

In this paper, the existence of solutions for discontinuous nonlinear parabolic differential IBVP is proved by using a more generalized monotone iterative method. Moreover, the convergence of this method is discussed.

关键词： discontinuous nonlinear equation monotone iterative method parabolic IBVP

A FINITE DIFFERENCE SCHEME FOR SOLVING THE NONLINEAR POISSON-BOLTZMANN EQUATION MODELING CHARGED SPHERES

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Journal of Computational Mathematics 2006年第3期24卷 252-264页

作者： Zhong-hua Qiao Zhi-lin Li Tao Tang Department of Mathematics Hong Kong Baptist University Kowloon Tong Hong Kong China Center for Research in Scientific Computation and Department of Mathematics North Carolina State University Raleigh NC 27695 USA

In this work, we propose an efficient numerical method for computing the electrostatic interaction between two like-charged spherical particles which is governed by the nonlinear Poisson-Boltzmann equation. The nonlinear problem is solved by a monotone iterative method which leads to a sequence of linearized equations. A modified central finite difference scheme is developed to solve the linearized equations on an exterior irregular domain using a uniform Cartesian grid. With uniform grids, the method is simple, and as a consequence, multigrid solvers can be employed to speed up the convergence. Numerical experiments on cases with two isolated spheres and two spheres confined in a charged cylindrical pore are carried out using the proposed method. Our numerical schemes are found efficient and the numerical results are found in good agreement with the previous published results.

关键词： Nonlinear Poisson-Boltzmann equation Electrostatic interaction Irregulardomain monotone iterative method Multigrid solver

THE EXISTENCE AND BLOW-UP OF THE RADIAL SOLUTIONS OF A(k_(1),k_(2))-HESSIAN SYSTEM INVOLVING A NONLINEAR OPERATOR AND GRADIENT

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Acta Mathematica Scientia 2022年第4期42卷 1414-1426页

作者： Guotao WANG Zedong YANG Jiafa XU Lihong ZHANG School of Mathematics and Computer Science Shanxi Normal UniversityTaiyuan 030031China School of Mathematical Sciences Chongqing Normal UniversityChongqing 401331China

In this paper,we are concerned with the existence of the positive bounded and blow-up radial solutions of the(k1,k2)-Hessian system■where G is a nonlinear operator,Ki=Ski(λ(D^(2) z_(i)))+ψ_(i)(|x|)|▽_(zi)|^(ki),i=1,*** the appropriate conditions on gi and g2,our main results are obtained by using the monotone iterative method and the Arzela-Ascoli ***,our main results also extend the previous existence results for both the single equation and systems.

关键词： (k_(1),k_(2))-Hessian system nonlinear operator blow-up monotone iterative method gradient

Existence and iteration of monotone positive solutions for a third-order two-point boundary value problem

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Applied Mathematics(A Journal of Chinese Universities) 2008年第4期23卷 413-419页

作者： SUN Yong-ping School of Electronics and Information Zhejiang University of Media and Communications Hangzhou 310018 China

The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t）＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied.... 详细信息

关键词： third-order two-point boundary value problem monotone iterative method positive solution,existence iterative scheme

Periodic boundary value problem for the first order functional differential equations with impulses

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Applied Mathematics(A Journal of Chinese Universities) 2009年第1期24卷 27-35页

作者： LIANG Rui-xi SHEN Jian-hua Dept. of Math. Hunan Normal Univ. Hunan 410081 China Dept. of Math. Huaihua College Hunan 418008 China

This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is pres... 详细信息

关键词： functional differential equation periodic boundary value problem lower and upper solution monotone iterative method

lassification and existence of positive entire k-convex radial solutions for generalized nonlinear k-Hessian system

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Applied Mathematics(A Journal of Chinese Universities) 2021年第4期36卷 564-582页

作者： ZHANG Li-hong YANG Ze-dong WANG Guo-tao Mohammad M.Rashidi School of Mathematics and Computer Science Shanxi Normal UniversityLinfen 041004China Shanghai Automotive Wind Tunnel Center Tongji UniversityShanghai 201804China

In this paper,we consider the following generalized nonlinear k-Hessian system G(S_(k)^(1/k)(λ(D^(2)z1)))S_(k)^(1/k)(λ(D^(2)z1))=φ(|x|,z1,z2),x∈R^(N),G(S_(k)^(1/k)(λ(D^(2)z2)))S_(k)^(1/k)(λ(D^(2)z2))=ψ(|x|,z1,z2),x∈R^(N),where G is a nonlinear operator and Sk(λ(D^(2)z))stands for the k-Hessian *** first are interested in the classification of positive entire k-convex radial solutions for the k-Hessian system ifφ(|x|,z1,z2)=b(|x|)φ(z1,z2)andψ(|x|,z1,z2)=h(|x|)ψ(z1).Moreover,with the help of the monotone iterative method,some new existence results on the positive entire k-convex radial solutions of the k-Hessian system with the special non-linearitiesψ,φare given,which improve and extend many previous works.

关键词： k-Hessian system entire blow-up classification of radial solutions monotone iterative method

EXTREME SOLUTIONS OF INITIAL VALUE PROBLEMS FOR NONLINEAR SECOND ORDER INTEGRODIFFERENTIAL EQUATIONS IN BANACH SPACES

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Acta Mathematicae Applicatae Sinica 2001年第3期17卷 289-295页

作者：陈芳启 Department of Mathematics Tianjin University Tianjin China Department of Mathematics Shandong University Jinan China

In this paper, using the monotone iterative method, we study the existence of extreme solutions of initial value problems for nonlinear second order integrodifferential equations in Banach spaces. Some existence theor... 详细信息

关键词： Iategrodifferential equations Kuratowski measure of noncompactness lower and upper solutions monotone iterative method

Existence of Solution for Fractional Differential Problem with a Parameter

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Communications in Mathematical Research 2014年第2期30卷 157-167页

作者： Shi Ai-ling Zhang Shu-qin Li Yong School of Science Beijing University of Civil Engineering and Architecture Department of Mathematics China University of Mining and Technology

We apply the method of lower and upper solutions combined with mono- tone iterations to fractional differential problem with a parameter. The existence of minimal and maximal solutions is proved for the fractional dif... 详细信息

关键词： Caputo derivative parameter monotone iterative method

monotone　iterative　Technique　for　Boundary　Value　Problem　of　Second　Order　Singular　Differential　System

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Systems Science and Systems Engineering 1995年第3期5卷 266-272页

作者： WANG Wei LIU Yongqing(Dept.of Automation,South China Univ.of Technology Guangzhou, 510641)

In this paper,boundary value problems(BVP for short) for second order singular differential equations are reduced to initial value problems(IVP for short)for first order singular integro-differential equations and the existence of external solutions of reduction IVP is given,in which f is increasing in the integral term,and thus one can obtain existence of solutions of second order problems.

关键词： singular differential equations singular integro-differential equations boundary value problem monotone iterative method