Smoothness of generalized solutions of the first boundary-value problem for an elliptic difference-differential equation

1983 ◽  
Vol 34 (1) ◽  
pp. 537-541 ◽  
Author(s):  
A. L. Skubachevskii
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Generalized Solutions ◽  
Elliptic Difference ◽  
Smoothness Of Generalized Solutions

scholarly journals Second-order neutrosophic boundary-value problem

2021 ◽  
Author(s):  
Sandip Moi ◽  
Suvankar Biswas ◽  
Smita Pal(Sarkar)
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Differential Calculus ◽  
Boundary Value ◽  
Second Order ◽  
Numerical Examples ◽  
Different Types ◽  
First Time

AbstractIn this article, some properties of neutrosophic derivative and neutrosophic numbers have been presented. This properties have been used to develop the neutrosophic differential calculus. By considering different types of first- and second-order derivatives, different kind of systems of derivatives have been developed. This is the first time where a second-order neutrosophic boundary-value problem has been introduced with different types of first- and second-order derivatives. Some numerical examples have been examined to explain different systems of neutrosophic differential equation.

On a Singular Two-Point Boundary Value Problem for the Nonlinear mth-Order Differential Equation with Deviating Arguments

1997 ◽  
Vol 4 (6) ◽  
pp. 557-566
Author(s):  
B. Půža
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Vector Function ◽  
Unique Solvability ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Point Boundary ◽  
Deviating Arguments ◽  
Measurable Functions

Abstract Sufficient conditions of solvability and unique solvability of the boundary value problem u (m)(t) = f(t, u(τ 11(t)), . . . , u(τ 1k (t)), . . . , u (m–1)(τ m1(t)), . . . . . . , u (m–1)(τ mk (t))), u(t) = 0, for t ∉ [a, b], u (i–1)(a) = 0 (i = 1, . . . , m – 1), u (m–1)(b) = 0, are established, where τ ij : [a, b] → R (i = 1, . . . , m; j = 1, . . . , k) are measurable functions and the vector function f : ]a, b[×Rkmn → Rn is measurable in the first and continuous in the last kmn arguments; moreover, this function may have nonintegrable singularities with respect to the first argument.

A New Method and Applications of the Boundary Value Problem of Differential Equation

2014 ◽  
Vol 937 ◽  
pp. 695-699
Author(s):  
Hong E Li ◽  
Xiao Xu Dong ◽  
Shun Chu Li ◽  
Dong Dong Gui ◽  
Cong Yin Fan
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Kernel Function ◽  
Boundary Value ◽  
Outer Boundary ◽  
Seepage Flow ◽  
Petroleum Engineering ◽  
Constructive Method ◽  
Linear Homogeneous Differential Equation ◽  
The Mathematical Model

The similar structure of solution for the boundary value problem of second order linear homogeneous differential equation has been studied. Based on the analysis of the relationship between similar structure of solution, its kernel function, the equation and boundary conditions, similar constructive method (shortened as SCM) of solution is obtained. According to the SCM, the similar structure of solution and its kernel function are constructed for the mathematical model of homogeneous reservoir which considers the influence of bottom-hole storage and skin effect under the infinite outer boundary condition. The SCM is a new and innovative way to solve boundary value problem of differential equation and seepage flow theory, which is especially used in Petroleum Engineering.

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