Effect of the domain geometry on the existence of multipeak solutions for an elliptic problem
Słowa kluczowe
Peaks, nonlinear, small diffusion, Conley index, Clarke derivativeAbstrakt
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 $T_i$, $i=1,\ldots,k$.Pobrania
Opublikowane
1999-09-01
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1.
DANCER, E. Norman & YAN, Shusen. Effect of the domain geometry on the existence of multipeak solutions for an elliptic problem. Topological Methods in Nonlinear Analysis [online]. 1 wrzesień 1999, T. 14, nr 1, s. 1–38. [udostępniono 22.7.2024].
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