On the existence of positive solutions for nonlinear differential equations with periodic boundary conditions
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In this paper, the existence of positive solutions of second-order nonlinear differential equations on a finite interval with periodic boundary conditions was proved and upper and lower bounds for these positive solutions were given.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2001-07-06 and is currently open access. It has received 86 citations till now. The article focuses on the topics: Boundary value problem & Differential equation.read more
Citations
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On Green's functions and positive solutions for boundary value problems on time scales
TL;DR: In this article, a form of self-adjoint differential equations on time scales so that the associated Green's function is found symmetric in the usual sense is presented. And the concepts of Lebesgue delta and nabla integrals are introduced.
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Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskii fixed point theorem
TL;DR: In this article, the existence of periodic solutions of the second-order Caratheodory problem is studied, by combining some new properties of Green's function together with Krasnoselskii fixed point theorem on compression and expansion of cones.
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Solving singular nonlinear second-order periodic boundary value problems in the reproducing kernel space
Fazhan Geng,Minggen Cui +1 more
TL;DR: A new method for solving a singular nonlinear second-order periodic boundary value problem in the form of series in the reproducing kernel space is presented and it is proved to converge to the analytical solution.
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Existence, multiplicity, and dependence on a parameter for a periodic boundary value problem
TL;DR: In this paper, the boundary value problem was considered in the context of boundary value maximization, where the authors considered the problem of finding a boundary value for a given set of variables.
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Numerical algorithm for solving two-point, second-order periodic boundary value problems for mixed integro-differential equations
Omar Abu Arqub,Mohammed Al-Smadi +1 more
TL;DR: The numerical result indicates that the proposed method for solving Fredholm-Volterra integro-differential equations for two-point, second-order periodic boundary value problems is straightforward to implement, efficient, and accurate for solving linear and nonlinear equations.
References
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Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
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On the existence of positive solutions of ordinary differential equations
L. H. Erbe,Haiyan Wang +1 more
TL;DR: In this article, the existence of positive solutions of the equation u" + a(t)f(u) = 0 with linear boundary conditions was studied and it was shown that there exists at least one positive solution if f is either superlinear or sublinear by a simple application of a fixed point theorem in cones.
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Multiple Positive Solutions of Some Boundary Value Problems
TL;DR: In this article, the existence of multiple positive solutions of the equations − u "′=ƒ( t, u ), subject to linear boundary conditions, was studied and it was shown that there are at least two positive solutions if ǫ( t, u ) is superlinear at one end point (zero or infinity) and sublinear at the other.