共查询到20条相似文献,搜索用时 15 毫秒
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We study the existence of positive solutions for the following boundary value problem on infinite interval for second-order functional differential equations:
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Using the mixed monotone method we establish the existence and uniqueness of positive solutions for coupled systems of second-order three-point non-linear differential and difference equations. The theorems obtained are very general and complement previously known results. 相似文献
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Christopher C. Tisdell 《International Journal of Mathematical Education in Science & Technology》2017,48(7):1087-1095
For over 50 years, the learning of teaching of a priori bounds on solutions to linear differential equations has involved a Euclidean approach to measuring the size of a solution. While the Euclidean approach to a priori bounds on solutions is somewhat manageable in the learning and teaching of the proofs involving second-order, linear problems with constant co-efficients, we believe it is not pedagogically optimal. Moreover, the Euclidean method becomes pedagogically unwieldy in the proofs involving higher-order cases. The purpose of this work is to propose a simpler pedagogical approach to establish a priori bounds on solutions by considering a different way of measuring the size of a solution to linear problems, which we refer to as the Uber size. The Uber form enables a simplification of pedagogy from the literature and the ideas are accessible to learners who have an understanding of the Fundamental Theorem of Calculus and the exponential function, both usually seen in a first course in calculus. We believe that this work will be of mathematical and pedagogical interest to those who are learning and teaching in the area of differential equations or in any of the numerous disciplines where linear differential equations are used. 相似文献
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A. D. Myshkis 《Mathematical Notes》1999,66(6):719-725
Multivalued (not set-valued as in the theory of differential inclusions!) solutions of ordinary differential equations (ODE)
appear naturally in geometrical and physical problems in which the independent and dependent variablesx, y are geometric coordinates of a current point on the sought-for curve. This note contains some simple results concerning smooth
multivalued solutions of real second-order ODE resolved with respect toy″; the special role of equations of the third degree with respect toy′ is underlined. The method of investigation is based on combining ODEs fory(x) andx(y).
Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 871–878, December, 1999. 相似文献
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Criteria are established for existence of multiple positive solutions to the boundary value problems expressed by second-order delay differential equations of the form
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C.C. Tisdell 《International Journal of Mathematical Education in Science & Technology》2017,48(6):913-918
Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem through a substitution. The purpose of this note is to present an alternative approach using ‘exact methods’, illustrating that a substitution and linearization of the problem is unnecessary. The ideas may be seen as forming a complimentary and arguably simpler approach to Azevedo and Valentino that have the potential to be assimilated and adapted to pedagogical needs of those learning and teaching exact differential equations in schools, colleges, universities and polytechnics. We illustrate how to apply the ideas through an analysis of the Gompertz equation, which is of interest in biomathematical models of tumour growth. 相似文献
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姚庆六 《应用泛函分析学报》2006,8(2):110-117
研究了2n阶Lidstone边值问题正解的逐次迭代,其中非线性项依赖于所有偶数阶导数.通过考察非线性项在某些有国介集合上的“高度”并利用单调迭代方法构造了一个逐次迭代程序.这个迭代程序从一个多项式开始并且是可行的.使用这个结论获得了m个正解的迭代方法,其中m是一个任意的自然数. 相似文献
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Stephen Clark Johnny Henderson 《Proceedings of the American Mathematical Society》2006,134(11):3363-3372
For the third order differential equation, we consider uniqueness implies existence results for solutions satisfying the nonlocal -point boundary conditions, Uniqueness of solutions of such boundary value problems is intimately related to solutions of the third order equation satisfying certain nonlocal -point boundary conditions. These relationships are investigated as well.
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Wu-jun Sun 《高校应用数学学报(英文版)》2010,25(1):9-17
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. 相似文献
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EXISTENCE AND UNIQUENESS FOR SECOND-ORDER VECTOR BOUNDARY VALUE PROBLEM OF NONLINEAR SYSTEMS 总被引:1,自引:0,他引:1
Du Zengji Lin Xiaojie Ge Weigao 《高校应用数学学报(英文版)》2005,20(3):323-330
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. 相似文献
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Positive solutions of three-point boundary value problems for systems of nonlinear second order ordinary differential equations 总被引:1,自引:0,他引:1
In this paper, we study the three-point boundary value problems for systems of nonlinear second order ordinary differential equations of the form Under some conditions, we show the existence and multiplicity of positive solutions of the above problem by applying the fixed point index theory in cones. 相似文献
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We aim at demonstrating a novel theorem on the derivation of energy integrals for linear second-order ordinary differential equations with variable coefficients. Namely, in this context, we will present a possible and consistent method to overcome the traditional difficulty of deriving energy integrals for Lagrangian functions that explicitly exhibit the independent variable. Our theorem is such that it appropriately governs the arbitrariness of the variable coefficients in order to have energy integrals ensured. In view of the theoretical framework in which the theorem will be embedded, we will also demonstrate that it can be applied as a mathematical method to solve linear second-order ordinary differential equations with variable coefficients. These results are expected to have a generalized fundamental character. 相似文献
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In this paper, we shall discuss the properties of the well-known Mittag-Leffler function, and consider the existence and uniqueness of solution of the initial value problem for fractional differential equation involving Riemann-Liouville sequential fractional derivative by using monotone iterative method. 相似文献
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姚庆六 《Annals of Differential Equations》2004,20(1):99-105
In this paper, we establish two existence theorems of twin positive solutions for a class of nonlinear second-order three-point boundary value problems, and concentrate on the case when nonlinear term does not satisfy usual conditions. 相似文献
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