Abstract
In this paper we consider the p-Laplace problem \( - {\varepsilon ^p}{\Delta _p}u + V\left( x \right){u^{p - 1}} = {u^{q - 1}},u{\text{ > }}0\) in RN where 2 ≤ p < N, ε > 0 and \(p{\text{ < }}q{\text{ < }}p* = \frac{{Np}}{{N - p}}\). V is a non-negative function satisfying certain conditions and ε is a small parameter. We obtain the existence of solutions concentrated near set consisting of disjoint components of zero set of V under certain assumptions on V when ε > 0 is small.
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Supported by the National Natural Science Foundation of China (No. 11371117) and the Natural Science Foundation of Hebei province (No. A2012402036).
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Zhang, Zh., Xu, Hy. Existence of multi-peak solutions for p-Laplace problems in ℝN . Acta Math. Appl. Sin. Engl. Ser. 31, 1061–1072 (2015). https://doi.org/10.1007/s10255-015-0528-7
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DOI: https://doi.org/10.1007/s10255-015-0528-7