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Periodic solutions for three-dimensional non-monotone cyclic systems with time delays
On the profile of solutions for an elliptic problem arising in nonlinear optics
| 1. | Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing, 100080, China |
| 2. | School of Mathematics, The University of New South Wales, Sydney 2052, Australia |
| 3. | School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia |
$-\Delta u + (\lambda - h(x)) u = g(x) (u^{p-1} + f(u))$ in $\ \mathbb R^N,$
$u > 0$ in $\mathbb R^N,$
$u \in H^1(\mathbb R^N),$
where $\lambda > 0$ is a parameter, $h$ and $g$ are nonnegative functions in $L^\infty(\mathbb R^N).$ We obtain the asymptotic behaviour of the least energy solutions or solutions obtained by the minimax principle. From the asymptotic behaviour we conclude that those solutions are asymmetric for $\lambda$ large even if $h$ and $g$ are radially symmetric.
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