scholarly journals Existence of Strong Solutions for Nonlinear Systems of PDEs Arising in Convective Flow

2022 ◽  
Vol 2022 ◽  
pp. 1-10
Author(s):  
Khaled Bouazzaoui ◽  
Mohammed Aiboudi ◽  
Sameh Elsayed Ahmed
Keyword(s):  
Porous Medium ◽  
Fixed Point ◽  
Nonlinear System ◽  
Fixed Point Theorem ◽  
Convective Flow ◽  
Strong Solutions ◽  
Fredholm Alternative ◽  
Flow Modeling ◽  
Systems Of Pdes ◽  
Second Order Elliptic Operators

In this paper, we will study the existence of strong solutions for a nonlinear system of partial differential equations arising in convective flow, modeling a phenomenon of mixed convection created by a heated and diving plate in a porous medium saturated with a fluid. The main tools are Schäfer’s fixed-point theorem, the Fredholm alternative, and some theorems on second-order elliptic operators.

scholarly journals Existence of Solutions of Abstract Nonlinear Mixed Functional Integrodifferential equation with nonlocal conditions

2017 ◽  
Vol 4 (1) ◽  
pp. 1-15
Author(s):  
Machindra B. Dhakne ◽  
Poonam S. Bora
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Integrodifferential Equation ◽  
Existence Of Solutions ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Fractional Power ◽  
Strong Solutions ◽  
Fractional Power Of Operators

Abstract In this paper we discuss the existence of mild and strong solutions of abstract nonlinear mixed functional integrodifferential equation with nonlocal condition by using Sadovskii’s fixed point theorem and theory of fractional power of operators.

scholarly journals Existence theorems for generalized vector equilibria with variable ordering relation

2016 ◽  
Vol 47 (4) ◽  
pp. 455-475
Author(s):  
Lu-Chuan Ceng ◽  
Yeong-Cheng Liou ◽  
Ching-Feng Wen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Existence Theorems ◽  
Strong Solutions ◽  
Existence Results ◽  
Reflexive Banach Spaces ◽  
Fan Theorem ◽  
Variable Ordering ◽  
Vector Equilibrium

In this paper we study the solvability of the generalized vector equilibrium problem (for short, GVEP) with a variable ordering relation in reflexive Banach spaces. The existence results of strong solutions of GVEPs for monotone multifunctions are established with the use of the KKM-Fan theorem. We also investigate the GVEPs without monotonicity assumptions and obtain the corresponding results of weak solutions by applying the Brouwer fixed point theorem. These results are also the extension and improvement of some recent results in the literature.

scholarly journals Existence of solutions and controllability of nonlinear integrodifferential systems in Banach spaces

2003 ◽  
Vol 2003 (2) ◽  
pp. 65-79 ◽  
Author(s):  
K. Balachandran ◽  
J. Y. Park
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Strong Solutions ◽  
Integrodifferential Equations ◽  
Schäuder Fixed Point Theorem

We prove the existence of mild and strong solutions of integrodifferential equations with nonlocal conditions in Banach spaces. Further sufficient conditions for the controllability of integrodifferential systems are established. The results are obtained by using the Schauder fixed-point theorem. Examples are provided to illustrate the theory.

scholarly journals Nonlocal Cauchy problem for nonlinear mixed integrodifferential equations

2010 ◽  
Vol 41 (4) ◽  
pp. 361-374
Author(s):  
H. L. Tidke ◽  
M. B. Dhakne
Keyword(s):  
Cauchy Problem ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Strong Solutions ◽  
Integrodifferential Equations ◽  
Nonlocal Cauchy Problem

The present paper investigates the existence and uniqueness of mild and strong solutions of a nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition. The results obtained by using Schauder fixed point theorem and the theory of semigroups.

Periodic Solutions of Almost Linear Volterra Integro-dynamic Equations on Periodic Time Scales

2015 ◽  
Vol 58 (1) ◽  
pp. 174-181 ◽  
Author(s):  
Youssef N. Raffoul
Keyword(s):  
Fixed Point ◽  
Nonlinear System ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Discrete Time ◽  
Dynamic Equations ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence Of Periodic Solutions

AbstractUsing Krasnoselskii’s fixed point theorem, we deduce the existence of periodic solutions of nonlinear system of integro-dynamic equations on periodic time scales. These equations are studied under a set of assumptions on the functions involved in the equations. The equations will be called almost linear when these assumptions hold. The results of this paper are new for the continuous and discrete time scales.

scholarly journals Existence and uniqueness of mild and strong solutions of nonlinear volterra integrodifferential equations in Banach spaces

2010 ◽  
Vol 43 (3) ◽  
Author(s):  
H. L. Tidke ◽  
M. B. Dhakne
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Semigroup Theory ◽  
Strong Solutions ◽  
Banach Fixed Point Theorem ◽  
Volterra Integrodifferential Equation

AbstractIn this paper we prove the existence and uniqueness of mild and strong solutions of a nonlinear Volterra integrodifferential equation with nonlocal condition. Our analysis is based on semigroup theory and Banach fixed point theorem and inequalities are established by Gronwall and B. G. Pachpatte.

scholarly journals Existence of solutions for neutral functional integrodifferential equations

2010 ◽  
Vol 41 (2) ◽  
pp. 117-128 ◽  
Author(s):  
R. Murugesu ◽  
S. Suguna
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Fractional Power ◽  
Strong Solutions ◽  
Integrodifferential Equations ◽  
Fractional Power Of Operators

In this paper, by using fractional power of operators and Sadovskii's fixed point theorem, we study the existence of mild and strong solutions of nonlinear neutral functional integrodifferential equations. The results we obtained are a generalization and continuation of the recent results on this issue.

POSITIVE SOLUTIONS FOR SYSTEMS OF M‐POINT NONLINEAR BOUNDARY VALUE PROBLEMS

2008 ◽  
Vol 13 (3) ◽  
pp. 357-370 ◽  
Author(s):  
Johnny Henderson ◽  
Sotiris K. Ntouyas ◽  
Ioannis K. Purnaras
Keyword(s):  
Fixed Point ◽  
Nonlinear System ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Boundary Value

Positive solutions (u(t), v(t)) are sought for the nonlocal (m‐point) nonlinear system of boundary value problems, u” + λa(t)f(v) = 0, v” + λb(t)g(u) = 0, for 0 < t < 1, and satisfying, u(0) = 0, u(1) = . An application of a Guo‐Krasnosel'skii fixed point theorem yields sufficient values of λ for which such positive solutions exist.

scholarly journals Existence of solutions of nonlinear integrodifferential equations with nonlocal conditions

2005 ◽  
Vol 36 (4) ◽  
pp. 327-335
Author(s):  
A. Anguraj ◽  
A. R. Navaneethan ◽  
T. S. Sukanya
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Existence Of Solutions ◽  
Initial Conditions ◽  
Existence Theorems ◽  
Nonlocal Conditions ◽  
Strong Solutions ◽  
Integrodifferential Equations ◽  
Nonlocal Initial Conditions

In this paper we prove the existence of mild and strong solutions of semilinear integrodifferential equations in Banach spaces with nonlocal initial conditions. We prove the existence theorems by using Schaefer's fixed point theorem.

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