EXISTENCE OF SOLUTIONS FOR THE FRACTIONAL (p, q)-LAPLACIAN PROBLEMS INVOLVING A CRITICAL SOBOLEV EXPONENT

• 作者: Fanfan CHEN Yang YANG
• 来源期刊: 数学物理学报（英文版）
• 年，卷（期）: 2020,（6）
• 页码范围: 1666-1678
• 页数: 13页
• 语种: 英文

摘要

In this article, we study the following fractional (p, q)-Laplacian equations in-volving the critical Sobolev exponent:(Pμ，λ){(-△)sp1u+(-△)s2qu = μ|u|q-2u +λ|u|p-2u+|u|P*s1-2u, in Ω，u = 0, inRN\Ω，where Ω∈ RN is a smooth and bounded domain,λ, μ＞ 0, 0 ＜ s2 ＜ s1 ＜ 1, 1 ＜ q ＜ p ＜N/s1 .We establish the existence of a non-negative nontrivial weak solution to (Pμ,λ) by using the Mountain Pass Theorem. The lack of compactness associated with problems involving critical Sobolev exponents is overcome by working with certain asymptotic estimates for minimizers.