| Abstract: |
| This is a joint work with Ryuji Kajikiya and Inbo Sim.
The bifurcation problem of positive solutions for the Moore-Nehari
differential equation $u''+h(x,\lambda)u^p=0$ in $(-1,1)$ with
$u(-1)=u(1)=0$ is considered, where $p>1$, $h(x,\lambda)=0$ for
$|x| < \lambda$ and $h(x,\lambda)=1$ for $\lambda \le |x| \le 1$ and
$\lambda\in (0,1)$ is a bifurcation parameter.
The problem has a unique even positive solution $U(x,\lambda)$ for each $\lambda \in (0,1)$.
It is shown that there exists a unique $\lambda_*\in (0,1)$ such that a non-even positive solution bifurcates at $\lambda_*$ from the curve $(\lambda,U(x,\lambda))$, where $\lambda_*$ is explicitly represented as a
function of $p$. |
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