scholarly journals On a Multivalued Differential Equation with Nonlocality in Time

2020 ◽  
Vol 48 (4) ◽  
pp. 703-718
Author(s):  
André Eikmeier ◽  
Etienne Emmrich
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Growth Conditions ◽  
The Other ◽  
Initial Value ◽  
Existence Of A Solution ◽  
Volterra Integral Operator ◽  
Kakutani Fixed Point ◽  
Kakutani Fixed Point Theorem

AbstractThe initial value problem for a multivalued differential equation is studied, which is governed by the sum of a monotone, hemicontinuous, coercive operator fulfilling a certain growth condition and a Volterra integral operator in time of convolution type with exponential decay. The two operators act on different Banach spaces where one is not embedded in the other. The set-valued right-hand side is measurable and satisfies certain continuity and growth conditions. Existence of a solution is shown via a generalisation of the Kakutani fixed-point theorem.

Solvability of initial value problems with fractional order differential equations in banach spaces by α-dense curves

2017 ◽  
Vol 20 (3) ◽  
Author(s):  
Gonzalo García
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Initial Value Problems ◽  
Existence Of Solutions ◽  
Initial Value ◽  
Measures Of Noncompactness ◽  
Fractional Order Differential Equations ◽  
Fractional Differential

AbstractIn this paper we study the existence of solutions for an initial value problem, posed in a given Banach space, with a fractional differential equation via densifiability techniques. For our goal, we will prove a new fixed point result (not based on measures of noncompactness) which is, in forms, a generalization of the well-known Darbo’s fixed point theorem but essentially different. Some illustrative examples are given.

scholarly journals Applications of Krasnoselskii-Dhage Type Fixed-Point Theorems to Fractional Hybrid Differential Equations

2021 ◽  
Vol 52 ◽  
Author(s):  
Habibulla Akhadkulov ◽  
Fahad Alsharari ◽  
Teh Yuan Ying
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Integral Operators ◽  
Existence Of A Solution ◽  
Hybrid Differential Equation ◽  
Hybrid Differential Equations

In this paper, we prove the existence of a solution of a fractional hybrid differential equation involving the Riemann-Liouville differential and integral operators by utilizing a new version of Kransoselskii-Dhage type fixed-point theorem obtained in [13]. Moreover, we provide an example to support our result.

scholarly journals Existence of a Short-Run Equilibrium of the Dixit-Stiglitz-Krugman Model

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Minoru Tabata ◽  
Nobuoki Eshima
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Nonlinear Operator ◽  
Wage Equation ◽  
Short Run ◽  
Kakutani Fixed Point ◽  
Kakutani Fixed Point Theorem

Each short-run equilibrium of the Dixit-Stiglitz-Krugman model is defined as a solution to the wage equation when the distributions of workers and farmers are given functions. We extend the discrete nonlinear operator contained in the wage equation as a set-valued operator. Applying the Kakutani fixed-point theorem to the set-valued operator, under the most general assumptions, we prove that the model has a short-run equilibrium.

A non-linear Goursat problem for a high order polyvibrating equation

1986 ◽  
Vol 102 (1-2) ◽  
pp. 159-172
Author(s):  
Andrzej Borzymowski
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Functional Equations ◽  
Goursat Problem ◽  
Common Point ◽  
Existence Of A Solution ◽  
Non Linear

SynopsisThis paper proves the existence of a solution of a non-linear Goursat problem for a partial differential equation of order 2p (p ≧ 2) with the boundary conditions given on 2p curves emanating from a common point. The problem is reduced to a system of integro-differential-functional equations and then Schauder's fixed point theorem is applied.

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