scholarly journals Remarks on weak solutions for a nonlocal parabolic problem

2006 ◽  
Vol 2006 ◽  
pp. 1-10 ◽  
Author(s):  
S. B. de Menezes
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Parabolic Problem ◽  
Galerkin Approximation ◽  
Diffusion Problem ◽  
Fixed Point Result ◽  
Nonlinear Diffusions

We prove a result on existence and uniqueness of weak solutions for a diffusion problem associated with nonlinear diffusions of nonlocal type studied by Chipot and Lovat (1999) by an application of the fixed point result of Schauder. Moreover, making use of Faedo-Galerkin approximation, coupled with some technical ideas, we establish a result on existence of periodic solution.

scholarly journals On Random Periodic Solution to a Neutral Stochastic Functional Differential Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Lili Gao ◽  
Litan Yan
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Fixed Point ◽  
Brownian Motion ◽  
Functional Differential Equation ◽  
Existence And Uniqueness ◽  
Banach Fixed Point Theorem ◽  
Stochastic Functional Differential Equation ◽  
Functional Differential ◽  
Stochastic Functional

In this paper, we consider the random periodic solution to a neutral stochastic functional differential equation driven by Brownian motion. We obtain the existence and uniqueness of the random periodic solution by Banach fixed point theorem. Moreover, we introduce two examples to illustrate our results.

scholarly journals Some Common Fixed Point Theorems in Complex Valuedb-Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Aiman A. Mukheimer
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Result ◽  
Complex Valued ◽  
Common Fixed Point Theorems

Azam et al. (2011), introduce the notion of complex valued metric spaces and obtained common fixed point result for mappings in the context of complex valued metric spaces. Rao et al. (2013) introduce the notion of complex valuedb-metric spaces. In this paper, we generalize the results of Azam et al. (2011), and Bhatt et al. (2011), by improving the conditions of contraction to establish the existence and uniqueness of common fixed point for two self-mappings on complex valuedb-metric spaces. Some examples are given to illustrate the main results.

scholarly journals Weak solutions to the time-fractional g-Navier–Stokes equations and optimal control

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sultana Ben Aadi ◽  
Khalid Akhlil ◽  
Khadija Aayadi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Fractional Derivative ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Galerkin Approximation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Fractional Derivative

Abstract In this paper, we introduce the g-Navier–Stokes equations with time-fractional derivative of order α ∈ ( 0 , 1 ) {\alpha\in(0,1)} in domains of ℝ 2 {\mathbb{R}^{2}} . We then study the existence and uniqueness of weak solutions by means of the Galerkin approximation. Finally, an optimal control problem is considered and solved.

scholarly journals Existence and Uniqueness of Almost Periodic Solutions for Neural Networks with Neutral Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Min Xu ◽  
Zengji Du ◽  
Kaige Zhuang
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Almost Periodic Solution ◽  
Almost Periodic Solutions ◽  
Almost Periodic

A class of neural networks system with neutral delays is investigated. The existence and uniqueness of almost periodic solution for the system are obtained by using fixed point theorem; we extend some results in the references.

scholarly journals Fixed Point Theorems and Uniqueness of the Periodic Solution for the Hematopoiesis Models

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Jun Wu ◽  
Yicheng Liu
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Continuous Function ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Functional Differential Equations ◽  
Equivalent Norm ◽  
Multiple Delays ◽  
Functional Differential ◽  
Continuous Function Space

We present some results to the existence and uniqueness of the periodic solutions for the hematopoiesis models which are described by the functional differential equations with multiple delays. Our methods are based on the equivalent norm techniques and a new fixed point theorem in the continuous function space.

On existence result of a class of nonlinear integral equation

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3593-3597
Author(s):  
Ravindra Bisht
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Existence Result ◽  
Nonlinear Integral Equation ◽  
Continuous Functions ◽  
Concave Functions ◽  
Real Numbers ◽  
Fixed Point Techniques ◽  
Uniqueness Of A Solution

Combining the approaches of functionals associated with h-concave functions and fixed point techniques, we study the existence and uniqueness of a solution for a class of nonlinear integral equation: x(t) = g1(t)-g2(t) + ? ?t,0 V1(t,s)h1(s,x(s))ds + ? ?T,0 V2(t,s)h2(s,x(s))ds; where C([0,T];R) denotes the space of all continuous functions on [0,T] equipped with the uniform metric and t?[0,T], ?,? are real numbers, g1, g2 ? C([0, T],R) and V1(t,s), V2(t,s), h1(t,s), h2(t,s) are continuous real-valued functions in [0,T]xR.

scholarly journals Fixed point theorems via Generalized WF-Contractions with applications

SeMA Journal ◽  
2021 ◽  
Author(s):  
Rosana Rodríguez-López ◽  
Rakesh Tiwari
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
New Class ◽  
Second Order Differential Equations ◽  
Fixed Point Result

AbstractThe aim of this paper is to introduce a new class of mixed contractions which allow to revise and generalize some results obtained in [6] by R. Gubran, W. M. Alfaqih and M. Imdad. We also provide an example corresponding to this class of mappings and show how the new fixed point result relates to the above-mentioned result in [6]. Further, we present an application to the solvability of a two-point boundary value problem for second order differential equations.

scholarly journals Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Jamilu Abubakar ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

Abstract This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

scholarly journals Existence and Ulam stability for implicit fractional q-difference equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Nadjet Laledj ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Ulam Stability ◽  
Uniqueness Of Solutions ◽  
Stability Results ◽  
Rassias Stability

AbstractThis paper deals with some existence, uniqueness and Ulam–Hyers–Rassias stability results for a class of implicit fractional q-difference equations. Some applications are made of some fixed point theorems in Banach spaces for the existence and uniqueness of solutions, next we prove that our problem is generalized Ulam–Hyers–Rassias stable. Two illustrative examples are given in the last section.

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