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Acta Mechanica Solida Sinica 1997年第3期10卷 255-261页

作者： Yan Xianggan Wu Jike, Department of Mechanics, Peking Unirersity, Bejing 100871. China ost.tau.ac.il

By the separation of singularity, a special Fourier series solution of the boundary value problem for plane is obtained, which can satisfy all boundary conditions and converges rapidly. II is proved that the solution is equal to the result of separation of variables. As a result, the non-linear characteristic equations resulting from the method of separation of variables are transformed into polynomial equations that can provide a foundation for approximate computation and asymptotic analysis.

关键词： separation of singularity series resolution method of separation of variables boundary value problem characteristic equation

AN EXPONENTIALLY FITTED DIFFERENCE SCHEME FOR THE HYPERBOLIC-HYPERBOLIC SINGULARLY PERTURBED INITIAL-boundary value problem

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Applied Mathematics and Mechanics(English Edition) 1991年第3期12卷 237-245页

作者：苏煜城林平 Nanjing University Nanjing

In this paper we discuss, an initial-boundary value problem of hyperbolic type with first derivative with respect to x. The asymptotic solution is constructed and its uniform validity is proved under weader compatibility conditions. Then we develop an exponentially fitted difference scheme and establish discrete energy inequality. Finally, we prove that the solution of difference problem uniformly converges to the solution of the original problem.

关键词： hyperbolic equation singular perturbation exponential fitting,difference scheme boundary value problem

OSCILLATION OF SOLUTIONS FOR A CLASS OF NONLINEAR NEUTRAL PARABOLIC DIFFERENTIAL EQUATIONS boundary value problem

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Applied Mathematics and Mechanics(English Edition) 2000年第5期21卷 585-590页

作者：王培光 Department of Mathematics Hebei University 071002 Baoding P R China

A class of nonlinear neutral partial differential equations,uas considered, and some oscillation criteria for such equations subject to two different boundary value conditions are established.

关键词： parabolic equation boundary value problem oscillation

On the existence and uniqueness of a nonlinear q-difference boundary value problem of fractional order

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International Journal of Modeling, Simulation, and Scientific Computing 2022年第1期13卷 265-284页

作者： Zouaoui Bekri Vedat Suat Erturk Pushpendra Kumar Laboratory of Fundamental and Applied Mathematics University of Oran 1 Ahmed Ben Bella Es-senia31000 OranAlgeria Department of Mathematics Ondokuz Mayis University Atakum-55200 SamsunTurkey Department of Mathematics and Statistics School of Basic and Applied Sciences Central University of Punjab Bathinda Punjab-151001India

In this research collection,we estimate the existence of the unique solution for the boundary value problem of nonlinear fractional q-difference equation having the given form c D^(ζ)_(q) v(t)−h(t,v(t))=0,0≤t≤1,α_(1)v(0)+β_(1)D_(q)v(0)=v(η1),α_(2)v(1)−β_(2)D_(q)v(1)=v(η2),where 1<ζ≤2,(η1,η2)∈(0,1)^(2),α_(i),β_(i)∈R(i=1,2),h∈C([0,1]×R,R)and c Dζq represents the Caputo-type nonclassical q-derivative of orderζ.We use well-known principal of Banach contraction,and Leray–Schauder nonlinear alternative to vindicate the unique solution existence of the given *** the applications,some examples are solved to justify our outcomes.

关键词： Fractional q-derivative principle of Banach contraction Leary-Schauder non-linear alternative existence and uniqueness boundary value problem

MIXED boundary value problem FOR SECOND－ORDER SYSTEM OF DIFFERENTIAL EQUATIONS OF THE ELLIPTIC TYPE

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Acta Mathematica Scientia 1995年第1期15卷 58-64页

作者：陈庆祥 Dept. of Math. Zhongshan University Guangzhou 510275 China

In this *** following ined boundary value problem for second-order system of differential equations of the elliptic type will be discussed to find the function u and v such that they satisfy:The solution of this problem is found by means of the theory of generalized analutic function and the integral equation method for solving boundary value problems.

关键词： elliptic type differential eguation boundary value problem

An Existence Theorem of Solution for a Singular Third-order Two-point boundary value problem

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Chinese Quarterly Journal of Mathematics 2008年第1期23卷 61-66页

作者：姚庆六 Department of Applied Mathematics Nanjing University of Finance and Economics

By constructing suitable Banach space, an existence theorem is established under a condition of linear growth for the third-order boundary value problem u″′（t）＋f（t,u（t）,u′（t））=0,0〈t〈1,u（0）=u′（0）=u′（1）=0, where the nonlinear term contains first and second derivatives of unknown function. In this theorem the nonlinear term f（t, u, v, w） may be singular at t = 0 and t = 1. The main ingredient is Leray-Schauder nonlinear alternative.

关键词： singular ordinary differential equation boundary value problem existence theorem nonlinear alternative

Dirichlet boundary value problem with variable growth

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Journal of Harbin Institute of Technology(New Series) 2004年第3期11卷 262-266页

作者：董增福付永强 Dept. of Mathematics Harbin Institute of Technology Harbin 150001 ChinaDept. of Mathematics Harbin Institute of Technology Harbin 150001 China

In this paper, we study higher order elliptic partial differential equations with variable growth, and obtain the existence of solutions in the setting of Wm,p（x） spaces by means of an abstract result for variational inequalities obtained by Gossez and Mustonen. Our result generalizes the corresponding one of Kováik and Rákosník.

关键词： boundary value problem elliptic partial differential equation variable growth

Multiple Positive Solutions to a Nonlinear Two-point boundary value problem with p-Laplacian

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Journal of Mathematical Research and Exposition 2006年第3期26卷 480-488页

作者：李志艳严树林葛渭高河海大学常州校区数理部江苏常州213022 常州工程职业技术学院江苏常州213004 北京理工大学应用数学系北京100081

By a simple application of a new three functionals fixed point theorem, sufficient conditions axe obtained to guarantee the existence of at least three positive solutions for p-Laplacian equation：（φp（u′））′ ＋ α（t）f（t,u（t）） = 0 subject to nonlinear boundary value conditions. An example is presented to illustrate the theory.

关键词： boundary value problem p-Laplacian operator positive solution the threefunctionals fixed point theorem.

POSITIVE SOLUTIONS TO A SINGULAR SECOND ORDER THREE-POINT boundary value problem

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Applied Mathematics and Mechanics(English Edition) 2002年第7期23卷 854-866页

作者：曲文波张中新武俊德 Department of Mathematics Harbin Institute of Technology Harbin 150001 P R China

A fixed point theorem is used to study a singular second order three-point boundary value problem. The problem is more general. Combining the method of constructing Green functions with operators defined piecewise, the existence result of positive solutions to a singular second order three-point boundary value problem is established. The nonlinearity can be allowed to change sign.

关键词： positive solution boundary value problem existence

EXISTENCE OF SOLUTION FOR boundary value problem OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

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Applied Mathematics(A Journal of Chinese Universities) 2007年第3期22卷 291-298页

作者： Su Xinwei Liu Landong Dept. of Math. China University of Mining and Technology Beijing 100083 China

This paper is concerned with the boundary value problem of a nonlinear fractional differential equation. By means of Schauder fixed-point theorem, an existence result of solution is obtained.

关键词： fractional differential equation boundary value problem Caputo's fractional derivative Schauder fixed-point theorem.