Positive Solutions of Impulsive Dynamic System on Time Scales

2012 ◽  
Vol 55 (1) ◽  
pp. 214-224
Author(s):  
Da-Bin Wang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Dynamic System ◽  
Positive Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Dynamic Equations ◽  
Existence Of Positive Solutions

AbstractIn this paper, some criteria for the existence of positive solutions of a class of systems of impulsive dynamic equations on time scales are obtained by using a fixed point theorem in cones.

scholarly journals Existence of positive solutions for second-order nonlinear neutral dynamic equations on time scales

2021 ◽  
Vol 7 (1) ◽  
pp. 20-29
Author(s):  
Faycal Bouchelaghem ◽  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Main Tool ◽  
Second Order ◽  
Dynamic Equations ◽  
Existence Of Positive Solutions ◽  
Neutral Dynamic Equations

AbstractIn this article we study the existence of positive solutions for second-order nonlinear neutral dynamic equations on time scales. The main tool employed here is Schauder’s fixed point theorem. The results obtained here extend the work of Culakova, Hanustiakova and Olach [12]. Two examples are also given to illustrate this work.

scholarly journals Existence of Positive Solutions forp-LaplacianDynamic Equations with Derivative on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Jinjun Fan ◽  
Liqing Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Dynamic Equations ◽  
Existence Of Positive Solutions

We consider the existence of positive solutions of nonlinearp-Laplaciandynamic equations with derivative on time scales. Applying the Avery-Peterson fixed point theorem, we obtain at least three positive solutions to the problem. An example is also presented to illustrate the applications of the obtained results.

scholarly journals Multiple Positive Symmetric Solutions top-Laplacian Dynamic Equations on Time Scales

2009 ◽  
Vol 2009 ◽  
pp. 1-27
Author(s):  
You-Hui Su ◽  
Can-Yun Huang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Dynamic Equations ◽  
Discrete Equations ◽  
Special Cases ◽  
Krasnosel’Skii’S Fixed Point Theorem

This paper makes a study on the existence of positive solution top-Laplacian dynamic equations on time scales𝕋. Some new sufficient conditions are obtained for the existence of at least single or twin positive solutions by using Krasnosel'skii's fixed point theorem and new sufficient conditions are also obtained for the existence of at least triple or arbitrary odd number positive solutions by using generalized Avery-Henderson fixed point theorem and Avery-Peterson fixed point theorem. As applications, two examples are given to illustrate the main results and their differences. These results are even new for the special cases of continuous and discrete equations, as well as in the general time-scale setting.

scholarly journals Existence of Positive Solutions for Third-Order -Point Boundary Value Problems with Sign-Changing Nonlinearity on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Fatma Tokmak ◽  
Ilkay Yaslan Karaca
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Point Boundary ◽  
Third Order ◽  
Existence Of Positive Solutions

A four-functional fixed point theorem and a generalization of Leggett-Williams fixed point theorem are used, respectively, to investigate the existence of at least one positive solution and at least three positive solutions for third-order -point boundary value problem on time scales with an increasing homeomorphism and homomorphism, which generalizes the usual -Laplacian operator. In particular, the nonlinear term is allowed to change sign. As an application, we also give some examples to demonstrate our results.

scholarly journals Positive Solutions for Third-Orderp-Laplacian Functional Dynamic Equations on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Wen Guan ◽  
Da-Bin Wang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Dynamic Equation ◽  
Dynamic Equations ◽  
Third Order ◽  
Existence Criteria

We study the following third-orderp-Laplacian functional dynamic equation on time scales:Φp(uΔ∇(t))∇+a(t)f(u(t),u(μ(t)))=0,t∈0,TT,  u(t)=φ(t),  t∈-r,0T,  uΔ(0)=uΔ∇(T)=0, andu(T)+B0(uΔ(η))=0. By applying the Five-Functional Fixed Point Theorem, the existence criteria of three positive solutions are established.

scholarly journals Solutions of Second-Orderm-Point Boundary Value Problems for Impulsive Dynamic Equations on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Xue Xu ◽  
Yong Wang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Dynamic Equations ◽  
Point Boundary

We study a general second-orderm-point boundary value problems for nonlinear singular impulsive dynamic equations on time scalesuΔ∇(t)+a(t)uΔ(t)+b(t)u(t)+q(t)f(t,u(t))=0,t∈(0,1),t≠tk,uΔ(tk+)=uΔ(tk)-Ik(u(tk)), andk=1,2,…,n,u(ρ(0))=0,u(σ(1))=∑i=1m-2αiu(ηi)‍.The existence and uniqueness of positive solutions are established by using the mixed monotone fixed point theorem on cone and Krasnosel’skii fixed point theorem. In this paper, the function items may be singular in its dependent variable. We present examples to illustrate our results.

scholarly journals Existence of Positive Solutions form-Point Boundary Value Problems on Time Scales

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Ying Zhang ◽  
ShiDong Qiao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Boundary Value ◽  
Point Boundary ◽  
One Dimensional ◽  
Existence Of Positive Solutions

We study the one-dimensionalp-Laplacianm-point boundary value problem(φp(uΔ(t)))Δ+a(t)f(t,u(t))=0,t∈[0,1]T,u(0)=0,u(1)=∑i=1m−2aiu(ξi), whereTis a time scale,φp(s)=|s|p−2s,p>1, some new results are obtained for the existence of at least one, two, and three positive solution/solutions of the above problem by usingKrasnosel′skll′sfixed point theorem, new fixed point theorem due to Avery and Henderson, as well as Leggett-Williams fixed point theorem. This is probably the first time the existence of positive solutions of one-dimensionalp-Laplacianm-point boundary value problem on time scales has been studied.

scholarly journals Positive Solutions for Discontinuous Systems via a Multivalued Vector Version of Krasnosel’skiĭ’s Fixed Point Theorem in Cones

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 451
Author(s):  
Rodrigo López Pouso ◽  
Radu Precup ◽  
Jorge Rodríguez-López
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Operator ◽  
Positive Solutions ◽  
Point Theorem ◽  
Discontinuous Systems ◽  
Second Order Differential Equations ◽  
Existence Of Positive Solutions ◽  
Vector Version ◽  
Krasnosel’Skii’S Fixed Point Theorem

We establish the existence of positive solutions for systems of second–order differential equations with discontinuous nonlinear terms. To this aim, we give a multivalued vector version of Krasnosel’skiĭ’s fixed point theorem in cones which we apply to a regularization of the discontinuous integral operator associated to the differential system. We include several examples to illustrate our theory.

scholarly journals Properties of Some Partial Dynamic Equations on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Deepak B. Pachpatte
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Time Scales ◽  
Point Theorem ◽  
Integral Inequality ◽  
Dynamic Equation ◽  
Dynamic Equations ◽  
Banach Fixed Point Theorem

The main objective of the paper is to study the properties of the solution of a certain partial dynamic equation on time scales. The tools employed are based on the application of the Banach fixed-point theorem and a certain integral inequality with explicit estimates on time scales.

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