Existence and uniqueness of solutions of boundary value problems for third order differential equations
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In this article, the uniqueness of solutions of a particular k-point boundary value problem implies the existence of solutions for any assignment of the boundary values cij, where 2 < k < n, x, < k, 0 < i < mi 1.About:
This article is published in Journal of Differential Equations.The article was published on 1970-01-01 and is currently open access. It has received 69 citations till now. The article focuses on the topics: Boundary value problem & Mixed boundary condition.read more
Citations
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On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order
Bashir Ahmad,S. Sivasundaram +1 more
TL;DR: The existence and uniqueness of solutions for a four-point nonlocal boundary value problem of nonlinear integro-differential equations of fractional order q ∈ (1, 2] are proved by applying some standard fixed point theorems.
Journal ArticleDOI
The existence of solution for a third-order two-point boundary value problem☆
Qingliu Yao,Yuqiang Feng +1 more
TL;DR: The lower and upper solutions method and the fixed-point theorem on cone are used to establish several existence results of a third-order two-point boundary value problem.
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Existence of solutions for three-point boundary value problems for second order equations
TL;DR: Shooting methods are employed to obtain solutions of the three-point boundary value problem for the second order equation, where y = f(x, y, y'), y(x 1 ) = y 1, y( x 3) -y(x 2 ), = y 2, where f: (a,b) × R 2 → R is continuous, α < x 1 < x 2 < x 3 < b, and y 1, y 2 ∈ R, and conditions are imposed implying that solutions of such problems are unique, when they exist as discussed by the authors.
References
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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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Ordinary differential equations
TL;DR: In this article, the Poincare-Bendixson theory is used to explain the existence of linear differential equations and the use of Implicity Function and fixed point Theorems.
Journal ArticleDOI
On $N$-parameter families and interpolation problems for nonlinear ordinary differential equations
TL;DR: In this paper, the existence of solutions of a system of ordinary differential equations satisfying interpolation conditions was investigated, and the notion of pseudoderivatives was introduced to generalize to interpolation problems involving some coincident points.
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