We study the asymptotic behaviour of positive groundstate solutions to the quasilinear elliptic equation [Figure not available: see fulltext.]where 1 < p< N, p< q< l< + ∞ and ε> 0 is a small parameter. For ε→ 0 , we give a characterization of asymptotic regimes as a function of the parameters q, l and N. In particular, we show that the behaviour of the groundstates is sensitive to whether q is less than, equal to, or greater than the critical Sobolev exponent p∗:=pNN-p.
Groundstate asymptotics for a class of singularly perturbed p-Laplacian problems in RN / Albalawi, W.; Mercuri, C.; Moroz, V.. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 199:1(2020), pp. 23-63. [10.1007/s10231-019-00865-6]
Groundstate asymptotics for a class of singularly perturbed p-Laplacian problems in RN
Mercuri C.;
2020
Abstract
We study the asymptotic behaviour of positive groundstate solutions to the quasilinear elliptic equation [Figure not available: see fulltext.]where 1 < p< N, p< q< l< + ∞ and ε> 0 is a small parameter. For ε→ 0 , we give a characterization of asymptotic regimes as a function of the parameters q, l and N. In particular, we show that the behaviour of the groundstates is sensitive to whether q is less than, equal to, or greater than the critical Sobolev exponent p∗:=pNN-p.
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