scholarly journals n-th Order Functional Problems with Resonance of Dimension One

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2384
Author(s):  
Erin Benham ◽  
Nickolai Kosmatov
Keyword(s):  
Boundary Value Problem ◽  
Linear Functional ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Constructive Method ◽  
Bounded Linear ◽  
Dimension One ◽  
Bounded Linear Functional ◽  
Existence Criteria ◽  
Functional Problems

We consider the nonlinear n-th order boundary value problem Lu=u(n)=f(t,u(t),u′(t),…,u(n−1)(t))=Nu given arbitrary bounded linear functional conditions Bi(u)=0, i=1,…,n and develop a method that allows us to study all such resonance problems of order one, as well as implementing a more general constructive method for deriving existence criteria in the framework of the coincidence degree method of Mawhin. We demonstrate applicability of the formalism by giving an example for n=4.

scholarly journals On a fractional-order p-Laplacian boundary value problem at resonance on the half-line with two dimensional kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
O. F. Imaga ◽  
S. A. Iyase
Keyword(s):  
Differential Operator ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Half Line ◽  
At Resonance ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Problem At Resonance

AbstractIn this work, we consider the solvability of a fractional-order p-Laplacian boundary value problem on the half-line where the fractional differential operator is nonlinear and has a kernel dimension equal to two. Due to the nonlinearity of the fractional differential operator, the Ge and Ren extension of Mawhin’s coincidence degree theory is applied to obtain existence results for the boundary value problem at resonance. Two examples are used to validate the established results.

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.

scholarly journals An Analysis on the Positive Solutions for a Fractional Configuration of the Caputo Multiterm Semilinear Differential Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Sh. Rezapour ◽  
B. Azzaoui ◽  
B. Tellab ◽  
S. Etemad ◽  
H. P. Masiha
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Caputo Fractional Derivatives ◽  
Control Functions ◽  
Existence Of Positive Solutions ◽  
Semilinear Differential Equation ◽  
The Given ◽  
Existence Criteria

In this paper, we consider a multiterm semilinear fractional boundary value problem involving Caputo fractional derivatives and investigate the existence of positive solutions by terms of different given conditions. To do this, we first study the properties of Green’s function, and then by defining two lower and upper control functions and using the wellknown Schauder’s fixed-point theorem, we obtain the desired existence criteria. At the end of the paper, we provide a numerical example based on the given boundary value problem and obtain its upper and lower solutions, and finally, we compare these positive solutions with exact solution graphically.

scholarly journals Periodic solutions of the boundary value problem for the nonlinear heat equation

1984 ◽  
Vol 30 (1) ◽  
pp. 99-110 ◽  
Author(s):  
M. N. Nkashama ◽  
M. Willem
Keyword(s):  
Boundary Value Problem ◽  
Heat Equation ◽  
Periodic Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Nonlinear Heat Equation

We prove the existence of generalized periodic solutions of the boundary value problem for the nonlinear heat equation. The proof is based on classical Leray-Schauder's techniques and coincidence degree.

Similar Constructing Method for Solving the Model of the Plane Radial Flow of Dual Permeability Reservoir

2013 ◽  
Vol 419 ◽  
pp. 43-50 ◽  
Author(s):  
Cong Yin Fan ◽  
Shun Chu Li ◽  
Dong Dong Gui ◽  
Ming Hu ◽  
Hui Chun Li
Keyword(s):  
Boundary Value Problem ◽  
Radial Flow ◽  
Boundary Value ◽  
Outer Boundary ◽  
Structural Formula ◽  
Constructive Method ◽  
Well Bore ◽  
Bottom Hole ◽  
Constant Rate ◽  
Seepage Model

A seepage model of producing at a constant rate, based on the three outer boundary (infinite, closed, constant value) conditions and regardless of the well-bore storage and skin effects, is established for the problem of the plane radial flow of dual permeability reservoirs. Firstly, we get dimensionless model by introducing the dimensionless variables. Second, we obtain a boundary value problem of ordinary differential equation in the Laplace space by using the Laplace transformation. Finally, we prove that the solution to the boundary value problem has similar structural formula. Therefore a new method for solving such seepage model is obtainedSimilar Constructive Method (shortened as SCM). And then, according to the modified numerical inversion formula of Stehfest, we draw the curves of bottom-hole under the three kinds of outer boundary conditions by using MATLAB.

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