| Abstract: |
| We consider the boundary value problem $u'' + \lambda h(x,\alpha) e^u = 0$ for $x \in (-1,1)$;
$u(-1) = u(1) = 0$,
where $\lambda$ is a positive parameter, $\alpha\in(0,1)$, $h(x,\alpha)=0$ for $x\in(-\alpha,\alpha)$, and $h(x,\alpha)=1$ for $\alpha \le |x| \le 1$.
We compute the Morse index of positive even solutions, and then
we prove the existence of an unbounded connected set of positive non-even solutions emanating from a symmetry-breaking bifurcation point.
This is a joint work with Kanako Manabe (JG Corporation). |
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