涉及分数阶拉普拉斯的Kirchhoff问题正解的存在性

Pub Date : 2015-10-29 DOI:10.4171/ZAA/1547

B. Ge, Chao Zhang

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引用次数: 6

摘要

本文的目的是建立以下分数阶kirchhoff型问题(1 + λ∫RN(∣∣(-∆)α 2u (x)∣∣2 + V (x)u2) dx)[(-∆)αu+ V (x)u] = f(u)在R中的正解的存在性，其中N≥2，λ≥0是参数，α∈(0,1)，(-∆)α表示分数阶拉普拉斯算子，f∈C(R+，R+)。利用变分方法结合适当的截断技术，得到了在不紧性条件下至少有一个正解的存在性。

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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Existence of a positive solution to Kirchhoff problems involving the fractional Laplacian

The goal of this paper is to establish the existence of a positive solution to the following fractional Kirchhoff-type problem ( 1 + λ ∫ RN (∣∣(−∆)α2 u(x)∣∣2 + V (x)u2) dx)[(−∆)αu+ V (x)u] = f(u) in R , where N ≥ 2, λ ≥ 0 is a parameter, α ∈ (0, 1), (−∆)α stands for the fractional Laplacian, f ∈ C(R+,R+). Using a variational method combined with suitable truncation techniques, we obtain the existence of at least one positive solution without compactness conditions.

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