Global Solutions in R2 for Three-Well Potential
碩士 === 國立臺灣大學 === 數學研究所 === 89 === In this paper, we study the vector-valued problem in R2 -Laplation U + DW(U)=0 where W is a symmetric potential with three wells of equal depth. We show the existence of nontrivial smooth solution with 3n-layers. By...
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| Format: | Others |
| Language: | en_US |
| Published: |
2001
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| Online Access: | http://ndltd.ncl.edu.tw/handle/06089066119796731124 |
| Summary: | 碩士 === 國立臺灣大學 === 數學研究所 === 89 === In this paper, we study the vector-valued problem in R2
-Laplation U + DW(U)=0
where W is a symmetric potential with three wells of equal depth. We show the existence of nontrivial smooth solution with
3n-layers. By a proper conformal mapping, the equation is transferred to the following equation.
-Laplation U + r^(-l)DW(U)=0 l = 2(n-1)/n
By the symmetry of 3n-layer solution, we can find a
nontrivial smooth solution with three layers over R2/{o}.
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