EXISTENCE AND CONCENTRATION OF SOLUTION FOR A NON-LOCAL REGIONAL SCHRÖDINGER EQUATION WITH COMPETING POTENTIALS
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DOI: 10.1017/s0017089518000289
Abstract: Abstract In this paper, we study the existence and concentration phenomena of solutions for the following non-local regional Schrödinger equation $$\begin{equation*} \left\{ \begin{array}{l} \epsilon^{2\alpha}(-\Delta)_\rho^{\alpha} u + Q(x)u = K(x)|u|^{p-1}u,\;\;\mbox{in}\;\; \mathbb{R}^n,\\ u\in H^{\alpha}(\mathbb{R}^n) \end{array} \right. \end{equation*}$$… read more here.
Keywords: local regional; non local; regional schr; existence concentration ... See more keywords