On the numerical solution for nonlinear elliptic equations with variable weight coefficients in an integral boundary conditions

In the paper the two-dimensional elliptic equation with integral boundary conditions is solved by finite difference method. The main aim of the paper is to investigate the conditions for the convergence of the iterative methods for the solution of system of nonlinear difference equations. With this purpose, we investigated the structure of the spectrum of the difference eigenvalue problem. Some sufficient conditions are proposed such that the real parts of all eigenvalues of the corresponding difference eigenvalue problem are positive. The proof of convergence of iterative method is based on the properties of the M-matrices not requiring the symmetry or diagonal dominance of the matrices. The theoretical statements are supported by the results of the numerical experiment.

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Sequential Derivatives of Nonlinearq-Difference Equations with Three-Pointq-Integral Boundary Conditions

Journal of Applied Mathematics ◽

10.1155/2013/605169 ◽

2013 ◽

Vol 2013 ◽

pp. 1-9 ◽

Cited By ~ 2

Author(s):

Nittaya Pongarm ◽

Suphawat Asawasamrit ◽

Jessada Tariboon

Keyword(s):

Boundary Conditions ◽

Difference Equations ◽

Contraction Mapping ◽

Sufficient Conditions ◽

Degree Theory ◽

Integral Boundary Conditions ◽

Integral Boundary ◽

Krasnoselskii’S Fixed Point Theorem ◽

Quantum Numbers ◽

Derivatives Of

This paper studies sufficient conditions for the existence of solutions to the problem of sequential derivatives of nonlinearq-difference equations with three-pointq-integral boundary conditions. Our results are concerned with several quantum numbers of derivatives and integrals. By using Banach's contraction mapping, Krasnoselskii's fixed-point theorem, and Leray-Schauder degree theory, some new existence results are obtained. Two examples illustrate our results.

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Boundary Value Problems of Fractional Order Differential Equation with Integral Boundary Conditions and Not Instantaneous Impulses

Journal of Function Spaces ◽

10.1155/2015/954925 ◽

2015 ◽

Vol 2015 ◽

pp. 1-9 ◽

Cited By ~ 9

Author(s):

Peiluan Li ◽

Changjin Xu

Keyword(s):

Boundary Conditions ◽

Fractional Order ◽

Fixed Point Theorems ◽

Order Differential Equation ◽

Mild Solutions ◽

Sufficient Conditions ◽

Integral Boundary Conditions ◽

Fractional Order Differential Equation ◽

Uniqueness Of Solutions ◽

Integral Boundary

We investigate the existence of mild solutions for fractional order differential equations with integral boundary conditions and not instantaneous impulses. By some fixed-point theorems, we establish sufficient conditions for the existence and uniqueness of solutions. Finally, two interesting examples are given to illustrate our theory results.

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POSITIVE SOLUTIONS OF NTH-ORDER BOUNDARY VALUE PROBLEMS WITH INTEGRAL BOUNDARY CONDITIONS

Mathematical Modelling and Analysis ◽

10.3846/13926292.2015.1020531 ◽

2015 ◽

Vol 20 (2) ◽

pp. 188-204 ◽

Cited By ~ 4

Author(s):

Ilkay Yaslan Karaca ◽

Fatma Tokmak Fen

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Boundary Value Problem ◽

Boundary Conditions ◽

Positive Solutions ◽

Point Theorem ◽

Boundary Value ◽

Sufficient Conditions ◽

Integral Boundary Conditions ◽

Integral Boundary

In this paper, by using double fixed point theorem and a new fixed point theorem, some sufficient conditions for the existence of at least two and at least three positive solutions of an nth-order boundary value problem with integral boundary conditions are established, respectively. We also give two examples to illustrate our main results.

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ON EXISTENCE OF SOLUTIONS FOR NONLINEAR Q-DIFFERENCE EQUATIONS WITH NONLOCAL Q-INTEGRAL BOUNDARY CONDITIONS

Mathematical Modelling and Analysis ◽

10.3846/13926292.2015.1088483 ◽

2015 ◽

Vol 20 (5) ◽

pp. 604-618 ◽

Cited By ~ 4

Author(s):

Ravi P. Agarwal ◽

Guotao Wang ◽

Bashir Ahmad ◽

Lihong Zhang ◽

Aatef Hobiny ◽

...

Keyword(s):

Boundary Conditions ◽

Existence Of Solutions ◽

Fixed Point Theory ◽

Sufficient Conditions ◽

Integral Boundary Conditions ◽

Point Theory ◽

Integral Boundary ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

The Given

In this paper, we discuss the existence of solutions for nonlinear qdifference equations with nonlocal q-integral boundary conditions. The first part of the paper deals with some existence and uniqueness results obtained by means of standard tools of fixed point theory. In the second part, sufficient conditions for the existence of extremal solutions for the given problem are established. The results are well illustrated with the aid of examples.

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The Eigenvalue Problem for Caputo Type Fractional Differential Equation with Riemann-Stieltjes Integral Boundary Conditions

Journal of Function Spaces ◽

10.1155/2018/2176809 ◽

2018 ◽

Vol 2018 ◽

pp. 1-9 ◽

Cited By ~ 6

Author(s):

Wenjie Ma ◽

Yujun Cui

Keyword(s):

Differential Equation ◽

Eigenvalue Problem ◽

Boundary Conditions ◽

Fractional Differential Equation ◽

Integral Boundary Conditions ◽

Stieltjes Integral ◽

Integral Boundary ◽

Krasnoselskii’S Fixed Point Theorem ◽

Existence And Nonexistence ◽

Fractional Differential

In this paper, we investigate the eigenvalue problem for Caputo fractional differential equation with Riemann-Stieltjes integral boundary conditions Dc0+θp(y)+μf(t,p(y))=0, y∈[0,1], p(0)=p′′(0)=0, p(1)=∫01p(y)dA(y), where Dc0+θ is Caputo fractional derivative, θ∈(2,3], and f:[0,1]×[0,+∞)→[0,+∞) is continuous. By using the Guo-Krasnoselskii’s fixed point theorem on cone and the properties of the Green’s function, some new results on the existence and nonexistence of positive solutions for the fractional differential equation are obtained.

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Positive solutions of nonlinear fourth order iterative differential equations with two-point and integral boundary conditions

Nonautonomous Dynamical Systems ◽

10.1515/msds-2020-0139 ◽

2021 ◽

Vol 8 (1) ◽

pp. 297-306

Author(s):

Bouzid Mansouri ◽

Abdelouaheb Ardjouni ◽

Ahcene Djoudi

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Boundary Conditions ◽

Positive Solutions ◽

Fourth Order ◽

Continuous Dependence ◽

Sufficient Conditions ◽

Integral Boundary Conditions ◽

Integral Boundary ◽

Iterative Differential Equations

Abstract This paper provides sufficient conditions to guarantee the existence, uniqueness and continuous dependence of positive solutions of a nonlinear fourth order iterative differential equations with two-point and integral boundary conditions. The main arguments are based on the Schauder fixed point theorem to prove the existence of a positive solution. As an application, we given an example to illustrate the obtained results.

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Positive solutions of semipositone singular fractional differential systems with a parameter and integral boundary conditions

Open Mathematics ◽

10.1515/math-2018-0055 ◽

2018 ◽

Vol 16 (1) ◽

pp. 581-596 ◽

Cited By ~ 24

Author(s):

Xinan Hao ◽

Huaqing Wang

Keyword(s):

Boundary Conditions ◽

Positive Solutions ◽

Sufficient Conditions ◽

Integral Boundary Conditions ◽

Integral Boundary ◽

Differential Systems ◽

Fractional Differential Systems ◽

Existence Of Positive Solutions ◽

Singular Fractional Differential Equations ◽

Fractional Differential

AbstractIn this paper, the existence of positive solutions for systems of semipositone singular fractional differential equations with a parameter and integral boundary conditions is investigated. By using fixed point theorem in cone, sufficient conditions which guarantee the existence of positive solutions are obtained. An example is given to illustrate the results.

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A Second-Order Nonlinear Problem with Two-Point and Integral Boundary Conditions

Georgian Mathematical Journal ◽

10.1515/gmj.1994.243 ◽

1994 ◽

Vol 1 (3) ◽

pp. 243-249

Author(s):

S. A. Brykalov

Keyword(s):

Boundary Conditions ◽

Sufficient Conditions ◽

Integral Boundary Conditions ◽

Nonlinear Boundary Conditions ◽

Nonlinear Ordinary Differential Equation ◽

Second Order ◽

Integral Boundary ◽

Functional Boundary ◽

Functional Boundary Conditions ◽

Monotone Solutions

Abstract The paper gives sufficient conditions for the existence and nonuniqueness of monotone solutions of a nonlinear ordinary differential equation of the second order subject to two nonlinear boundary conditions one of which is two-point and the other is integral. The proof is based on an existence result for a problem with functional boundary conditions obtained by the author in [Brykalov, Differential Equations 27: 1415-1420, 1991].

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