| Abstract: |
| We study the Moore-Nehari differential equation.
For a nonnegative integer $n$, we call a solution $u$ an $n$-nodal solution if it has exactly $n$ zeros in
$(-1,1)$. We call a solution $u$ symmetric if it is even or odd.
We shall show that for each nonnegative integer $n$,
the equation has a unique $n$-nodal symmetric solution.
We call a solution $u$ an $(m,n)$ solution if it has exactly $m$ zeros in $(-1,0)$ and
exactly $n$ zeros in $(0,1)$.
We shall prove that for each nonnegative integers $m, n$,
the equation has an $(m,n)$-solution and an $(m,m)$-asymmetric solution. |
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