MHB Proving the Uniqueness of Solutions to Autonomous Systems: A Study on λ and R_n

  • Thread starter Thread starter onie mti
  • Start date Start date
  • Tags Tags
    Systems
onie mti
Messages
42
Reaction score
0
i am studying autonomous system, i came across this proposition
λ is in R and vector b is in R_n where the IVP

x' = Ax + c , with x(λ) = b has at most one solution

is it possible to prove this
 
Physics news on Phys.org
It is possible to prove this. What tools are available to you? For example, are you allowed to use the standard existence and uniqueness theorem where the hypotheses involve Lipschitz functions?
 

Thread 'A question about variables of integration'

I have the equation ##F^x=m\frac {d}{dt}(\gamma v^x)##, where ##\gamma## is the Lorentz factor, and ##x## is a superscript, not an exponent. In my textbook the solution is given as ##\frac {F^x}{m}t=\frac {v^x}{\sqrt {1-v^{x^2}/c^2}}##. What bothers me is, when I separate the variables I get ##\frac {F^x}{m}dt=d(\gamma v^x)##. Can I simply consider ##d(\gamma v^x)## the variable of integration without any further considerations? Can I simply make the substitution ##\gamma v^x = u## and then...
View full post »

Similar threads

I Can the Second Plane Autonomous System Have a Unique Critical Point?
  • · Replies 1 ·
Replies
1
Views
2K
A Can the Cauchy-Kovalewskaya Theorem Predict Solution Existence in All Cases?
  • · Replies 0 ·
Replies
0
Views
2K
Find the solutions of the system, for all λ
  • · Replies 7 ·
Replies
7
Views
1K
MHB Existence of Unique Solution for Nonlinear System with Arbitrary Constants
  • · Replies 1 ·
Replies
1
Views
1K
A Help with understanding why limit implies uniqueness
  • · Replies 1 ·
Replies
1
Views
2K
A Existence of unique solutions to a first order ODE on this interval
  • · Replies 2 ·
Replies
2
Views
2K
Prove that solutions to autonomous first order DE can't have local maxima
  • · Replies 2 ·
Replies
2
Views
1K
I Fundamental matrix of a second order 2x2 system of ODEs
  • · Replies 2 ·
Replies
2
Views
4K
I On the approximate solution obtained through Euler's method
  • · Replies 1 ·
Replies
1
Views
3K
A About ellipticity and a proof that a system of PDEs is elliptic
  • · Replies 0 ·
Replies
0
Views
2K