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• W2336993996 abstract "In this paper, we are concerned with theexistence of least energy solutions of nonlinear Schrodingerequations involving the half Laplacianbegin{eqnarray}(-Delta)^{1/2}u(x)+lambda V(x)u(x)=u(x)^{p-1}, u(x)geq 0,quad xin R^N,end{eqnarray}for sufficiently large $lambda$,$2 < p < frac{2N}{N-1}$ for $N geq 2$. $V(x)$ is a real continuous function on $R^N$. Using variational methods we prove the existence of least energy solution$u(x)$ which localize near the potential well int$(V^{-1}(0))$ for$lambda$ large. Moreover, if the zero sets int$(V^{-1}(0))$ of $V(x)$ include more than one isolated components, then $u_lambda(x)$ will be trapped around all the isolated components. However, in Laplacian case, when the parameter $lambda$ large, the corresponding least energy solution will be trapped around only one isolated component and become arbitrary small in other components of int$(V^{-1}(0))$. This is the essential difference with the Laplacian problems since the operator $(-Delta)^{1/2}$ is nonlocal." @default.
• W2336993996 created "2016-06-24" @default.
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• W2336993996 date "2016-04-01" @default.
• W2336993996 modified "2023-10-16" @default.
• W2336993996 title "Least energy solutions of nonlinear Schrödinger equations involving the half Laplacian and potential wells" @default.
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• W2336993996 doi "https://doi.org/10.3934/cpaa.2016.15.1215" @default.
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