An application of Tychonoff's fixed point theorem to hyperbolic partial differential equations

1965 ◽  
Vol 162 (1) ◽  
pp. 77-82 ◽  
Author(s):  
A. K. Aziz ◽  
J. P. Maloney
Keyword(s):  
Fixed Point ◽  
Partial Differential Equations ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential

scholarly journals Existence and Uniqueness of Mild Solutions to Impulsive Nonlocal Cauchy Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Mohamed Hannabou ◽  
Khalid Hilal ◽  
Ahmed Kajouni
Keyword(s):  
Fixed Point ◽  
Partial Differential Equations ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Cauchy Problems ◽  
Partial Differential ◽  
Krasnoselskii’S Fixed Point Theorem

In this paper, a class of nonlocal impulsive differential equation with conformable fractional derivative is studied. By utilizing the theory of operators semigroup and fractional derivative, a new concept on a solution for our problem is introduced. We used some fixed point theorems such as Banach contraction mapping principle, Schauder’s fixed point theorem, Schaefer’s fixed point theorem, and Krasnoselskii’s fixed point theorem, and we derive many existence and uniqueness results concerning the solution for impulsive nonlocal Cauchy problems. Some concrete applications to partial differential equations are considered. Some concrete applications to partial differential equations are considered.

scholarly journals Some Remarks on Transformations in Metric Spaces

1965 ◽  
Vol 8 (5) ◽  
pp. 659-666 ◽  
Author(s):  
James S. W. Wong
Keyword(s):  
Fixed Point ◽  
Partial Differential Equations ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Metric Spaces ◽  
Present Note ◽  
Existence Theorems ◽  
Special Case

Recently A. Haimovici [1] has proved a general fixed point theorem of transformations in metric spaces from which he obtained existence theorems for certain types of ordinary and partial differential equations. However, both the result and the proof are given for a rather special case. One of the purposes of this present note is to put his result on a more concrete basis and give a stronger characterization of the kind of transformations used in [l]. (Theorem 3).

scholarly journals Stability of a Class of Impulsive Neutral Stochastic Functional Partial Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yue Liu ◽  
Dehao Ruan
Keyword(s):  
Fixed Point ◽  
Brownian Motion ◽  
Partial Differential Equations ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Exponential Stability ◽  
Partial Differential ◽  
The Fixed Point Theorem ◽  
Moment Exponential Stability ◽  
Stochastic Functional

In this paper, a class of impulsive neutral stochastic functional partial differential equations driven by Brownian motion and fractional Brownian motion is investigated. Under some suitable assumptions, the pth moment exponential stability is discussed by means of the fixed-point theorem. Our results also improve and generalize some previous studies. Moreover, one example is given to illustrate our main results.

scholarly journals Multiplicity of positive periodic solutions to second order differential equations

2006 ◽  
Vol 73 (2) ◽  
pp. 175-182 ◽  
Author(s):  
Jifeng Chu ◽  
Xiaoning Lin ◽  
Daqing Jiang ◽  
Donal O'Regan ◽  
R. P. Agarwal
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Positive Periodic Solution ◽  
Second Order ◽  
Positive Periodic Solutions ◽  
Second Order Differential Equations

In this paper, we study the existence of positive periodic solutions to the equation x″ = f (t, x). It is proved that such a equation has more than one positive periodic solution when the nonlinearity changes sign. The proof relies on a fixed point theorem in cones.

scholarly journals Analysis of Implicit Type Nonlinear Dynamical Problem of Impulsive Fractional Differential Equations

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Naveed Ahmad ◽  
Zeeshan Ali ◽  
Kamal Shah ◽  
Akbar Zada ◽  
Ghaus ur Rahman
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Nonlocal Boundary ◽  
Dynamical Problem ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

We study the existence, uniqueness, and various kinds of Ulam–Hyers stability of the solutions to a nonlinear implicit type dynamical problem of impulsive fractional differential equations with nonlocal boundary conditions involving Caputo derivative. We develop conditions for uniqueness and existence by using the classical fixed point theorems such as Banach fixed point theorem and Krasnoselskii’s fixed point theorem. For stability, we utilized classical functional analysis. Also, an example is given to demonstrate our main theoretical results.

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