Effect of the domain geometry on the existence of multipeak solutions for an elliptic problem
Keywords
Peaks, nonlinear, small diffusion, Conley index, Clarke derivativeAbstract
In this paper, we construct multipeak solutions for a singularly perturbed Dirichlet problem. Under the conditions that the distance function $d(x,\partial\Omega)$ has $k$ isolated compact connected critical sets $T_1,\ldots,T_k$ satisfying $d(x,\partial\Omega) =c_j=\hbox{const.}$, for all $x\in T_j$, $\min_{i\ne j}d(T_i,T_j)> 2\max_{1\le j\le k}d(T_j,\partial\Omega)$, and the critical group of each critical set $T_i$ is nontrivial, we construct a solution which has exactly one local maximum point in a small neighbourhood of $T_i$, $i=1,\ldots,k$.Downloads
Published
1999-09-01
How to Cite
1.
DANCER, E. Norman and YAN, Shusen. Effect of the domain geometry on the existence of multipeak solutions for an elliptic problem. Topological Methods in Nonlinear Analysis. Online. 1 September 1999. Vol. 14, no. 1, pp. 1 - 38. [Accessed 20 September 2024].
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