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• W2334190442 abstract "For $k =1,cdots,K,$ let $M_k$ be a $q_k$-dimensional smooth compact framed manifold in $R^N$ with $q_k in {1,cdots,N-1} $.We consider the equation $-varepsilon^2Delta u + V(x)u - u^p = 0$ in$R^N$ where for each $k in {1,cdots,K}$ and some $m_k > 0,$$V(x)=|textrm{dist}(x,M_k)|^{m_k}+O(|textrm{dist}(x,M_k)|^{m_k+1})$ as $textrm{dist}(x,M_k) to 0 $.For a sequence of $varepsilon$ convergingto zero, we will find a positive solution $u_{varepsilon}$ of the equationwhich concentrates on $M_1cup dots cup M_K$." @default.
• W2334190442 created "2016-06-24" @default.
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• W2334190442 date "2015-03-01" @default.
• W2334190442 modified "2023-09-27" @default.
• W2334190442 title "Standing wave concentrating on compact manifolds for nonlinear Schrödinger equations" @default.
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• W2334190442 doi "https://doi.org/10.3934/cpaa.2015.14.825" @default.
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