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| For $N \le 3,$ we consider the following singularly perturbed elliptic system
\[
\left\{ \begin{array}{rl}
\varepsilon^2\Delta u_1 - W_1(x)u_1 + \mu_1 (u_1)^3 +\beta u_1 (u_2)^2= 0, \ \ u_1 > 0 &\text{ in }\bf{R}^N,\\
\varepsilon^2 \Delta u_2 - W_2(x)u_2 +\mu_2 (u_2)^3 +\beta u_2(u_1)^2 = 0, \ \ u_2 > 0 &\text{ in }\bf{R}^N.\\
\end{array} \right.
\]
For certain minmax values of a limiting problem, we show that
there exist one bump vector solutions corresponding to the minimax values.
This is a joint work with Kazunaga Tanaka in Waseda University. |
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