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\\label{1}\n  \\left\\{\\begin{split} \\mathcal{L}u\\: &= \\lambda u,~~u>0~ \\text{in} ~\\Omega,\n  u&=0~~\\text{in} ~~{U^c},\n  \\mathcal{N}_s(u)&=0 ~~\\text{in} ~~{\\mathcal{N}},\n  \\frac{\\partial u}{\\partial \\nu}&=0 ~~\\text{in}~~ \\partial \\Omega \\cap \\overline{\\mathcal{N}},\n  \\end{split} \\right.\\tag{$P_\\lambda$} \\end{equation}\n  where $U= (\\Omega \\cup 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