scholarly journals Monotone Iterative Technique for Partial Dynamic Equations of First Order on Time Scales

2008 ◽  
Vol 2008 ◽  
pp. 1-7 ◽  
Author(s):  
Peiguang Wang ◽  
Ping Li
Keyword(s):  
Time Scales ◽  
Monotone Iterative Technique ◽  
Dynamic Equations ◽  
Iterative Technique ◽  
First Order ◽  
Monotone Iterative ◽  
Comparison Results

This work is concerned with the monotone iterative technique for partial dynamic equations of first order on time scales and for this purpose, the existence, uniqueness, and comparison results are also established.

scholarly journals Existence and Iteration of Positive Solutions to Third-Order BVP for a Class ofp-Laplacian Dynamic Equations on Time Scales

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
A. Kameswara Rao
Keyword(s):  
Positive Solutions ◽  
Time Scales ◽  
Monotone Iterative Technique ◽  
Dynamic Equations ◽  
Laplacian Operator ◽  
Iterative Technique ◽  
Third Order ◽  
Iterative Schemes ◽  
Monotone Iterative ◽  
Existence Of Positive Solutions

We investigate the existence and iteration of positive solutions for the following third-orderp-Laplacian dynamic equations on time scales:(ϕp(uΔΔ(t)))∇+q(t)f(t,u(t),uΔΔ(t))=0,  t∈[a,b],αu(ρ(a))-βuΔ(ρ(a))=0,  γu(b)+δuΔ(b)=0,  uΔΔ(ρ(a))=0,whereϕp(s)isp-Laplacian operator; that is,ϕp(s)=sp-2s,  p>1,  ϕp-1=ϕq, and1/p+1/q=1.By applying the monotone iterative technique and without the assumption of the existence of lower and upper solutions, we not only obtain the existence of positive solutions for the problem, but also establish iterative schemes for approximating the solutions.

scholarly journals Terminal value problems of impulsive integro-differential equations in Banach spaces

1997 ◽  
Vol 10 (1) ◽  
pp. 71-78 ◽  
Author(s):  
Dajun Guo
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Banach Spaces ◽  
Mixed Type ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
First Order ◽  
Monotone Iterative ◽  
Equations Of Mixed Type ◽  
Nonnegative Solutions

This paper uses cone theory and the monotone iterative technique to investigate the existence of minimal nonnegative solutions of terminal value problems for first order nonlinear impulsive integro-differential equations of mixed type in a Banach space.

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