Find a continuous function on $mathbb{R}$ such that the following initial value problem has two solutions
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$dot{x}=f(x)$ , $x(0)=0$ When I limit myself to functions that are continuous on all of the real numbers I can only think of function with 1 unique solution or infinite solutions. Could someone give me an example with two different solutions?
ordinary-differential-equations
edited Jan 20 at 15:08
Bernard
121k740116
asked Jan 20 at 15:01
RogerRoger
847
$endgroup$
add a comment |
$begingroup$
$dot{x}=f(x)$ , $x(0)=0$ When I limit myself to functions that are continuous on all of the real numbers I can only think of function with 1 unique solution or infinite solutions. Could someone give me an example with two different solutions?
ordinary-differential-equations
edited Jan 20 at 15:08
Bernard
121k740116
asked Jan 20 at 15:01
RogerRoger
847
$endgroup$
1
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The standard example for the difference of Cauchy-Peano and Picard-Lindelöf is $dot x=2sqrt{|x|}$ or similar.
$endgroup$
– LutzL
Jan 20 at 16:07
add a comment |
$begingroup$
$dot{x}=f(x)$ , $x(0)=0$ When I limit myself to functions that are continuous on all of the real numbers I can only think of function with 1 unique solution or infinite solutions. Could someone give me an example with two different solutions?
ordinary-differential-equations
edited Jan 20 at 15:08
Bernard
121k740116
asked Jan 20 at 15:01
RogerRoger
847
$endgroup$
$dot{x}=f(x)$ , $x(0)=0$ When I limit myself to functions that are continuous on all of the real numbers I can only think of function with 1 unique solution or infinite solutions. Could someone give me an example with two different solutions?
ordinary-differential-equations
ordinary-differential-equations
edited Jan 20 at 15:08
Bernard
121k740116
asked Jan 20 at 15:01
RogerRoger
847
edited Jan 20 at 15:08
Bernard
121k740116
asked Jan 20 at 15:01
RogerRoger
847
edited Jan 20 at 15:08
Bernard
121k740116
edited Jan 20 at 15:08
Bernard
121k740116
edited Jan 20 at 15:08
Bernard
121k740116
121k740116
asked Jan 20 at 15:01
RogerRoger
847
asked Jan 20 at 15:01
RogerRoger
847
asked Jan 20 at 15:01
RogerRoger
847
847
1
$begingroup$
The standard example for the difference of Cauchy-Peano and Picard-Lindelöf is $dot x=2sqrt{|x|}$ or similar.
$endgroup$
– LutzL
Jan 20 at 16:07
add a comment |
1
$begingroup$
The standard example for the difference of Cauchy-Peano and Picard-Lindelöf is $dot x=2sqrt{|x|}$ or similar.
$endgroup$
– LutzL
Jan 20 at 16:07
1
1
$begingroup$
The standard example for the difference of Cauchy-Peano and Picard-Lindelöf is $dot x=2sqrt{|x|}$ or similar.
$endgroup$
– LutzL
Jan 20 at 16:07
$begingroup$
The standard example for the difference of Cauchy-Peano and Picard-Lindelöf is $dot x=2sqrt{|x|}$ or similar.
$endgroup$
– LutzL
Jan 20 at 16:07
add a comment |
0
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$begingroup$
The standard example for the difference of Cauchy-Peano and Picard-Lindelöf is $dot x=2sqrt{|x|}$ or similar.
$endgroup$
– LutzL
Jan 20 at 16:07