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.

A non-linear Goursat problem for a 4th order polyvibrating equation

1982 ◽  
Vol 92 (1-2) ◽  
pp. 153-164 ◽  
Author(s):  
Andrzej Borzymowski
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Functional Equations ◽  
Goursat Problem ◽  
Common Point ◽  
Order Partial Differential Equation ◽  
Non Linear

SynopsisIn the paper the existence is proved of a solution of a non-linear Goursat problem for a 4th order partial differential equation with the boundary conditions given on four curves emanating from a common point. The problem is reduced to a system of integro-functional equations and then Schauder's fixed point theorem is applied.

scholarly journals Controllability of semilinear stochastic evolution equations in Hilbert space

2001 ◽  
Vol 14 (4) ◽  
pp. 329-339 ◽  
Author(s):  
P. Balasubramaniam ◽  
J. P. Dauer
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Evolution Equations ◽  
Stochastic Partial Differential Equation ◽  
Semigroup Theory ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations

Controllability of semilinear stochastic evolution equations is studied by using stochastic versions of the well-known fixed point theorem and semigroup theory. An application to a stochastic partial differential equation is 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 Solution of a Goursat Problem in Optimal Domains

2007 ◽  
Vol 14 (1) ◽  
pp. 195-202
Author(s):  
Wolfgang Tutschke
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Function Space ◽  
Goursat Problem ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Optimal Subset ◽  
Domain Of Existence ◽  
Linear Differential

Abstract In case a non-linear differential equation is reduced to a fixed-point problem, one has to apply a fixed-point theorem to a suitably chosen subset of the underlying function space. Generally speaking, in view of the non-linearity of the differential equation the restrictions for the data of the problem will be the more extensive the greater the chosen subset of the function space. The problem is to find an optimal subset leading to a domain of existence for the desired solution being as large as possible. The present paper will discuss this question for a Goursat problem.

Unique Solution for Multi-point Fractional Integro-Differential Equations

2020 ◽  
Vol 21 (2) ◽  
pp. 219-226
Author(s):  
Chengbo Zhai ◽  
Lifang Wei
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Unique Solution ◽  
Existence And Uniqueness ◽  
Iterative Sequence ◽  
Point Boundary ◽  
Uniqueness Of Solutions

AbstractWe study a fractional integro-differential equation subject to multi-point boundary conditions: $$\left\{\begin{array}{l} D^\alpha_{0^+} u(t)+f(t,u(t),Tu(t),Su(t))=b,\ t\in(0,1),\\u(0)=u^\prime(0)=\cdots=u^{(n-2)}(0)=0,\\ D^p_{0^+}u(t)|_{t=1}=\sum\limits_{i=1}^m a_iD^q_{0^+}u(t)|_{t=\xi_i},\end{array}\right.$$where $\alpha\in (n-1,n],\ n\in \textbf{N},\ n\geq 3,\ a_i\geq 0,\ 0<\xi_1<\cdots<\xi_m\leq 1,\ p\in [1,n-2],\ q\in[0,p],b>0$. By utilizing a new fixed point theorem of increasing $\psi-(h,r)-$ concave operators defined on special sets in ordered spaces, we demonstrate existence and uniqueness of solutions for this problem. Besides, it is shown that an iterative sequence can be constructed to approximate the unique solution. Finally, the main result is illustrated with the aid of an example.

Cauchy's Problem in a Non-Linear Partial Differential Equation of Hyperbolic Type

1935 ◽  
Vol 31 (2) ◽  
pp. 195-202 ◽  
Author(s):  
M. Raziuddin Siddiqi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Linear Partial Differential Equation ◽  
Positive Function ◽  
Hyperbolic Type ◽  
Partial Differential ◽  
Non Linear ◽  
Image Position

Let p (x) be an essentially positive function defined in the interval 0 ≤ x ≤ π. We consider the non-linear partial differential equationfor the boundary conditions u (x, t) = 0,for x = 0 and x = π,

Existence result for nonlinear fractional differential equations with nonlocal fractional integro-differential boundary conditions in Banach spaces

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Djamila Seba ◽  
Hamza Rebai ◽  
Johnny Henderson
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Banach Spaces ◽  
Fractional Differential Equations ◽  
Existence Result ◽  
Nonlinear Fractional Differential Equation ◽  
Measures Of Noncompactness ◽  
Fractional Differential

Abstract The nonlinear fractional differential equation with nonlocal fractional integro-differential boundary conditions in Banach spaces is studied, an existence result is obtained by using the method associated with the technique of measures of noncompactness and an appropriate fixed point theorem. An example is given to illustrate the theory.

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.

scholarly journals Mild Solution for a Stochastic Partial Differential Equation with Noise

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
White Noise ◽  
Mild Solution ◽  
Point Theorem ◽  
Stochastic Partial Differential Equation ◽  
Stochastic Equation ◽  
Multiplicative White Noise

This paper focuses on the study of the existence of a mild solution to time and space-fractional stochastic equation perturbed by multiplicative white noise. The required results are obtained by means of Sadovskii’s fixed point theorem.

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