Abstract
We consider the problem \({\varepsilon^{2}\Delta u - u^q + u^p = 0\,{\rm in}\,\Omega,\,u > 0\,{\rm in}\,\Omega,\,\frac{\partial u}{\partial \nu} = 0\,{\rm on}\,\partial\Omega }\) where Ω is a smooth bounded domain in \({\mathbb{R}^N}\) , \({1 < q < p < {N+2\over N-2}}\) if N ≥ 2 and \({\varepsilon}\) is a small positive parameter. We determine the location and shape of the least energy solution when \({\varepsilon \rightarrow 0.}\)
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Santra, S., Wei, J. Profile of the least energy solution of a singular perturbed Neumann problem with mixed powers. Annali di Matematica 193, 39–70 (2014). https://doi.org/10.1007/s10231-012-0265-y
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DOI: https://doi.org/10.1007/s10231-012-0265-y