On the Existence of Weak Solutions of Nonlinear Integral Equations in Banach Spaces

2015 ◽  
Vol 13 (5) ◽  
pp. 2633-2643 ◽  
Author(s):  
Baolin Li ◽  
Haide Gou
Keyword(s):  
Banach Spaces ◽  
Integral Equations ◽  
Weak Solutions ◽  
Nonlinear Integral Equations ◽  
Existence Of Weak Solutions

Weak compactness of Fréchet-derivatives: application to composition operators

1980 ◽  
Vol 29 (4) ◽  
pp. 399-406
Author(s):  
Peter Dierolf ◽  
Jürgen Voigt
Keyword(s):  
Banach Spaces ◽  
Integral Equations ◽  
Sobolev Spaces ◽  
Composition Operators ◽  
Weak Compactness ◽  
Nonlinear Integral Equations ◽  
Weakly Compact ◽  
Frechet Derivatives ◽  
Fréchet Derivatives ◽  
Compact Map

AbstractWe prove a result on compactness properties of Fréchet-derivatives which implies that the Fréchet-derivative of a weakly compact map between Banach spaces is weakly compact. This result is applied to characterize certain weakly compact composition operators on Sobolev spaces which have application in the theory of nonlinear integral equations and in the calculus of variations.

scholarly journals Weak Solutions of a Coupled System of Urysohn-Stieltjes Functional (Delayed) Integral Equations

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
A. M. A. El-Sayed ◽  
M. M. A. Al-Fadel
Keyword(s):  
Banach Space ◽  
Integral Equations ◽  
Weak Solutions ◽  
Reflexive Banach Space ◽  
Coupled System ◽  
Functional Integral ◽  
Existence Of Weak Solutions ◽  
Functional Integral Equations ◽  
Stieltjes Type

We study the existence of weak solutions for the coupled system of functional integral equations of Urysohn-Stieltjes type in the reflexive Banach spaceE. As an application, the coupled system of Hammerstien-Stieltjes functional integral equations is also studied.

scholarly journals Weak Solutions for Partial Random Hadamard Fractional Integral Equations with Multiple Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Yong Zhou ◽  
Ahmed Alsaedi
Keyword(s):  
Integral Equations ◽  
Weak Solutions ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Functional Integral ◽  
Multiple Delays ◽  
Measure Of Weak Noncompactness ◽  
Existence Of Weak Solutions ◽  
Functional Integral Equations ◽  
Hadamard Fractional Integral

We present some results concerning the existence of weak solutions for some functional integral equations of Hadamard fractional order with random effects and multiple delays by applying Mönch’s and Engl’s fixed point theorems associated with the technique of measure of weak noncompactness.

Elliptic problems in generalized Orlicz-Musielak spaces

2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Piotr Gwiazda ◽  
Piotr Minakowski ◽  
Aneta Wróblewska-Kamińska
Keyword(s):  
Boundary Value Problem ◽  
Banach Spaces ◽  
Elliptic Problem ◽  
Weak Solutions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Dirichlet Boundary Value Problem ◽  
Hölder Continuous ◽  
Existence Of Weak Solutions ◽  
Strongly Nonlinear

AbstractWe consider a strongly nonlinear monotone elliptic problem in generalized Orlicz-Musielak spaces. We assume neither a Δ2 nor ∇2-condition for an inhomogeneous and anisotropic N-function but assume it to be log-Hölder continuous with respect to x. We show the existence of weak solutions to the zero Dirichlet boundary value problem. Within the proof the L ∞-truncation method is coupled with a special version of the Minty-Browder trick for non-reflexive and non-separable Banach spaces.

scholarly journals Existence of Tripled Fixed Points for a Class of Condensing Operators in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Vatan Karakaya ◽  
Nour El Houda Bouzara ◽  
Kadri Doğan ◽  
Yunus Atalan
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Integral Equations ◽  
Existence Of Solutions ◽  
General System ◽  
Nonlinear Integral Equations ◽  
Condensing Operators

We give some results concerning the existence of tripled fixed points for a class of condensing operators in Banach spaces. Further, as an application, we study the existence of solutions for a general system of nonlinear integral equations.

scholarly journals Existence of Weak Solutions for Caputo’s Fractional Derivatives in Banach Spaces

2019 ◽  
Vol 39 ◽  
pp. 111-118
Author(s):  
Samima Akhter
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Weak Solutions ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Existence Of Weak Solutions

The objective of this project is to represent the existence of solutions for Caputo’s fractional derivatives in Banach spaces. The result is based on some well-known fixed point theorems. To show the efficiency of the stated result some examples will be demonstrated GANIT J. Bangladesh Math. Soc.Vol. 39 (2019) 111-118

scholarly journals Weak solutions for nonlinear fractional differential equation with fractional separated boundary conditions in Banach spaces

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 1117-1125 ◽  
Author(s):  
Hamza Rebai ◽  
Djamila Seba
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Banach Spaces ◽  
Fractional Differential Equation ◽  
Weak Solutions ◽  
Nonlinear Fractional Differential Equation ◽  
Existence Of Weak Solutions ◽  
Separated Boundary Conditions ◽  
Fractional Differential ◽  
Measures Of Weak Noncompactness

This paper deals with nonlinear fractional differential equation with fractional separated boundary conditions. We investigate the existence of weak solutions in Banach spaces. To obtain such result we apply an appropriate fixed point theorem and the technique of measures of weak noncompactness. An example illustrating the theory is given.

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