Let $y' = g(t,y)sin^2(y)$, discuting limit of solution.
$begingroup$
Let $y' = g(t,y)sin^2(y)$, with $ g: mathbb{R} times mathbb{R}to mathbb{R}$, g differentiable.
I want to prove that if a solution is maximal, there exists the limits $lim_{tto pm infty} y(t)$.
This is what I have done: product of differentiable functions is still differentiable, so I can say that there exists a local solution and it is unique.Then there also exists a maximal solution that is unique.
To try and calculate that limit I must also say that the maximal solutions are globally defined on all $mathbb{R}$, which is where I am stuck. Besides, even assuming that I know this fact, I would not know how to continue.
Any hint?
ordinary-differential-equations initial-value-problems
asked Jan 12 at 15:40
qcc101qcc101
594213
$endgroup$
add a comment |
$begingroup$
Let $y' = g(t,y)sin^2(y)$, with $ g: mathbb{R} times mathbb{R}to mathbb{R}$, g differentiable.
I want to prove that if a solution is maximal, there exists the limits $lim_{tto pm infty} y(t)$.
This is what I have done: product of differentiable functions is still differentiable, so I can say that there exists a local solution and it is unique.Then there also exists a maximal solution that is unique.
To try and calculate that limit I must also say that the maximal solutions are globally defined on all $mathbb{R}$, which is where I am stuck. Besides, even assuming that I know this fact, I would not know how to continue.
Any hint?
ordinary-differential-equations initial-value-problems
asked Jan 12 at 15:40
qcc101qcc101
594213
$endgroup$
add a comment |
$begingroup$
Let $y' = g(t,y)sin^2(y)$, with $ g: mathbb{R} times mathbb{R}to mathbb{R}$, g differentiable.
I want to prove that if a solution is maximal, there exists the limits $lim_{tto pm infty} y(t)$.
This is what I have done: product of differentiable functions is still differentiable, so I can say that there exists a local solution and it is unique.Then there also exists a maximal solution that is unique.
To try and calculate that limit I must also say that the maximal solutions are globally defined on all $mathbb{R}$, which is where I am stuck. Besides, even assuming that I know this fact, I would not know how to continue.
Any hint?
ordinary-differential-equations initial-value-problems
asked Jan 12 at 15:40
qcc101qcc101
594213
$endgroup$
Let $y' = g(t,y)sin^2(y)$, with $ g: mathbb{R} times mathbb{R}to mathbb{R}$, g differentiable.
I want to prove that if a solution is maximal, there exists the limits $lim_{tto pm infty} y(t)$.
This is what I have done: product of differentiable functions is still differentiable, so I can say that there exists a local solution and it is unique.Then there also exists a maximal solution that is unique.
To try and calculate that limit I must also say that the maximal solutions are globally defined on all $mathbb{R}$, which is where I am stuck. Besides, even assuming that I know this fact, I would not know how to continue.
Any hint?
ordinary-differential-equations initial-value-problems
ordinary-differential-equations initial-value-problems
asked Jan 12 at 15:40
qcc101qcc101
594213
asked Jan 12 at 15:40
qcc101qcc101
594213
asked Jan 12 at 15:40
qcc101qcc101
594213
asked Jan 12 at 15:40
qcc101qcc101
594213
asked Jan 12 at 15:40
qcc101qcc101
594213
594213
add a comment |
add a comment |
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