三维临界非局部问题的正基态解

Pub Date : 2022-06-01 DOI:10.4208/jpde.v35.n4.6

X. Qian

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引用次数: 0

摘要

．本文研究具有临界指数的非局部问题，其中a, b为正常数，2 < p < 6， Ω为r3中的光滑有界区域，λ > 0为参数。用变分方法证明了当λ > 0足够大时，问题有一个正的基态解。此外，我们以b为参数，研究了当b接近于0时u b的渐近行为。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Positive Ground State Solutions for a Critical Nonlocal Problem in Dimension Three

. In this paper, we are interested in the following nonlocal problem with critical exponent where a , b are positive constants, 2 < p < 6, Ω is a smooth bounded domain in R 3 and λ > 0 is a parameter. By variational methods, we prove that problem has a positive ground state solution u b for λ > 0 sufﬁciently large. Moreover, we take b as a parameter and study the asymptotic behavior of u b when b ց 0.

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