Existence and Uniqueness of Solutions of Second Order Nonlinear Differential Equations

1983 ◽  
Vol 14 (3) ◽  
pp. 477-487 ◽  
Author(s):  
James T. Sandefur, Jr.
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Nonlinear Differential Equations ◽  
Second Order ◽  
Uniqueness Of Solutions

scholarly journals On Solution of Two-Point Fuzzy Boundary Value Problems

2014 ◽  
Vol 11 ◽  
pp. 31-39 ◽  
Author(s):  
Hülya Gültekin ◽  
Nihat Altinişik
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Second Order ◽  
Uniqueness Of Solutions ◽  
Fuzzy Boundary Value Problems ◽  
Fuzzy Boundary

In this paper, we investigate the existence and uniqueness of solutions of two-point fuzzy boundary value problems for second-order fuzzy differential equations. Some sufficient conditions are presented that guarantee the existence and uniqueness of solutions under the approach of Hukuhara differentiability.

scholarly journals SOME LINEAR AND NONLINEAR EQUATIONS OF HIGHER ORDER

2016 ◽  
pp. 46-52
Author(s):  
Nadezda Chuesheva ◽  
Nadezda Chuesheva ◽  
Aleksandr Chueshev ◽  
Aleksandr Chueshev
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Nonlinear Equations ◽  
Existence And Uniqueness ◽  
Nonlinear Differential Equations ◽  
Uniqueness Of Solutions ◽  
Partial Derivatives ◽  
Petviashvili Equation ◽  
De Vries ◽  
Linear And Nonlinear

In this article we consider boundary value problems for some linear and nonlinear differential equations with partial derivatives of the sixth, fifth, fourth and third orders. We write out conditions on equation coefficients for which existence and uniqueness of solutions from Sobolev's space occur. If these conditions on equation coefficients are not valid, then there are given examples when solution is not unique, or is not unstable, or does not belong to Sobolev's space from existence and uniqueness theorem even for analytical coefficients and analytical right side of differential equation. After S.P. Novikov’s fundamental study in 1974 the interest to the nonlinear Korteweg-de Vries equation, Kadomtsev-Petviashvili equation and other nonlinear equations significantly grew. In this study of such equations we used methods of algebraic geometry integration and expansion method. In these studies exact solutions of special nonlinear equations series in partial derivatives play a big role. Solvability of similar equations was also studied in articles of A.I. Kozhanov, N.A. Larkin and other authors. The aim of this article is to find some exact solutions for special series partial differential equations. Solution graphs of such problems for linear equations and for the Korteweg-de Vries, Burgers-Korteweg-deVries, and Kadomtsev-Petviashvili equations are constructed.

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