Geodesic
EXISTENCE AND CONCENTRATION OF SOLUTION FOR A NON-LOCAL REGIONAL SCHRÖDINGER EQUATION WITH COMPETING POTENTIALS
Glasgow mathematical journal, Tome 61 (2019) no. 2, pp. 441-460

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In this paper, we study the existence and concentration phenomena of solutions for the following non-local regional Schrödinger equation$$\begin{equation*}\left\{\begin{array}{l}\epsilon^{2\alpha}(-\Delta)_\rho^{\alpha} u + Q(x)u = K(x)|u|^{p-1}u,\;\;\mbox{in}\;\; \mathbb{R}^n,\\u\in H^{\alpha}(\mathbb{R}^n)\end{array}\right.\end{equation*}$$where ε is a positive parameter, 0 < α < 1, $1, n > 2α; (−Δ)ρα is a variational version of the regional fractional Laplacian, whose range of scope is a ball with radius ρ(x) > 0, ρ, Q, K are competing functions. 
ALVES, CLAUDIANOR O.; LEDESMA, CÉSAR E. TORRES. EXISTENCE AND CONCENTRATION OF SOLUTION FOR A NON-LOCAL REGIONAL SCHRÖDINGER EQUATION WITH COMPETING POTENTIALS. Glasgow mathematical journal, Tome 61 (2019) no. 2, pp. 441-460. doi: 10.1017/S0017089518000289
@article{10_1017_S0017089518000289,
     author = {ALVES, CLAUDIANOR O. and LEDESMA, C\'ESAR E. TORRES},
     title = {EXISTENCE {AND} {CONCENTRATION} {OF} {SOLUTION} {FOR} {A} {NON-LOCAL} {REGIONAL} {SCHR\"ODINGER} {EQUATION} {WITH} {COMPETING} {POTENTIALS}},
     journal = {Glasgow mathematical journal},
     pages = {441--460},
     year = {2019},
     volume = {61},
     number = {2},
     doi = {10.1017/S0017089518000289},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089518000289/}
}
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