| Citation: |
Jianqing Chen, Xiuli Tang. A NON-RADIALLY SYMMETRIC SOLUTION TO A CLASS OF ELLIPTIC EQUATION WITH KIRCHHOFF TERM[J]. Journal of Applied Analysis & Computation, 2019, 9(4): 1558-1570. doi: 10.11948/2156-907X.20180340
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A NON-RADIALLY SYMMETRIC SOLUTION TO A CLASS OF ELLIPTIC EQUATION WITH KIRCHHOFF TERM
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Abstract
We consider the following equation with Kirchhoff term $ -(a+b\int_{\mathbb{R}^3} {|\nabla u|^2} dx) $ $ \Delta u + u = |u|^{p-2}u $, $ u \in H^1 (\mathbb{R}^3) $, where $ a, b $ are positive constants and $ 2 < p < 6 $. By deducing a variant variational identity and a constraint set, we are able to prove the existence of a non-radially symmetric solution $ u(x_1, x_2, x_3) $ for the full range of $ p\in (2, 6) $. Moreover this solution $ u(x_1, x_2, x_3) $ is radially symmetric with respect to $ (x_1, x_2) $ and odd with respect to $ x_3 $. -
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References
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Jianqing Chen, Xiuli Tang. A NON-RADIALLY SYMMETRIC SOLUTION TO A CLASS OF ELLIPTIC EQUATION WITH KIRCHHOFF TERM[J]. Journal of Applied Analysis & Computation, 2019, 9(4): 1558-1570. doi: 10.11948/2156-907X.20180340
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