Examples on Picard-LindelöfâÂÂs theorem for odes
Clash Royale CLAN TAG#URR8PPP
up vote
0
down vote
favorite
I am trying to find an example of ode, $x^âÂÂ=f(t,x)$, where $f$ does not satisfies Picard-Lindelöf theorem, but it still have unique solution.
Is it possible?
differential-equations
add a comment |Â
up vote
0
down vote
favorite
I am trying to find an example of ode, $x^âÂÂ=f(t,x)$, where $f$ does not satisfies Picard-Lindelöf theorem, but it still have unique solution.
Is it possible?
differential-equations
You can look at Alexander Eremenko's answer to Solution set of non-unique solutions to First order ODE's on MO.
â user539887
Aug 10 at 19:10
And if you need a concrete example, see, e.g., Example: f(x,y) is not Lipschitz in y but still has a unique solution to initial value problem.
â user539887
Aug 11 at 8:00
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am trying to find an example of ode, $x^âÂÂ=f(t,x)$, where $f$ does not satisfies Picard-Lindelöf theorem, but it still have unique solution.
Is it possible?
differential-equations
I am trying to find an example of ode, $x^âÂÂ=f(t,x)$, where $f$ does not satisfies Picard-Lindelöf theorem, but it still have unique solution.
Is it possible?
differential-equations
asked Aug 10 at 18:25
Charles
533420
533420
You can look at Alexander Eremenko's answer to Solution set of non-unique solutions to First order ODE's on MO.
â user539887
Aug 10 at 19:10
And if you need a concrete example, see, e.g., Example: f(x,y) is not Lipschitz in y but still has a unique solution to initial value problem.
â user539887
Aug 11 at 8:00
add a comment |Â
You can look at Alexander Eremenko's answer to Solution set of non-unique solutions to First order ODE's on MO.
â user539887
Aug 10 at 19:10
And if you need a concrete example, see, e.g., Example: f(x,y) is not Lipschitz in y but still has a unique solution to initial value problem.
â user539887
Aug 11 at 8:00
You can look at Alexander Eremenko's answer to Solution set of non-unique solutions to First order ODE's on MO.
â user539887
Aug 10 at 19:10
You can look at Alexander Eremenko's answer to Solution set of non-unique solutions to First order ODE's on MO.
â user539887
Aug 10 at 19:10
And if you need a concrete example, see, e.g., Example: f(x,y) is not Lipschitz in y but still has a unique solution to initial value problem.
â user539887
Aug 11 at 8:00
And if you need a concrete example, see, e.g., Example: f(x,y) is not Lipschitz in y but still has a unique solution to initial value problem.
â user539887
Aug 11 at 8:00
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
1
down vote
accepted
Yes, it is.
- Osgood's criterion
- $f(t,x)$ is decreasing as a function of $x$ for all $t$.
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
Yes, it is.
- Osgood's criterion
- $f(t,x)$ is decreasing as a function of $x$ for all $t$.
add a comment |Â
up vote
1
down vote
accepted
Yes, it is.
- Osgood's criterion
- $f(t,x)$ is decreasing as a function of $x$ for all $t$.
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
Yes, it is.
- Osgood's criterion
- $f(t,x)$ is decreasing as a function of $x$ for all $t$.
Yes, it is.
- Osgood's criterion
- $f(t,x)$ is decreasing as a function of $x$ for all $t$.
answered Aug 10 at 18:43
Julián Aguirre
64.9k23894
64.9k23894
add a comment |Â
add a comment |Â
Â
draft saved
draft discarded
Â
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2878682%2fexamples-on-picard-lindel%25c3%25b6f-s-theorem-for-odes%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
You can look at Alexander Eremenko's answer to Solution set of non-unique solutions to First order ODE's on MO.
â user539887
Aug 10 at 19:10
And if you need a concrete example, see, e.g., Example: f(x,y) is not Lipschitz in y but still has a unique solution to initial value problem.
â user539887
Aug 11 at 8:00