Concentration-compactness principle for nonlocal scalar field equations with critical growth

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• 作者：Joã ; o Marcos do Ó ; ; ^{jmbo@pq.cnpq.br} ; Diego Ferraz ^{diego.ferraz.br@gmail.com}
• 关键词：Scalar field equation ; Fractional Laplacian ; Concentration-compactness
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 May 2017
• 年：2017
• 卷：449
• 期：2
• 页码：1189-1228
• 全文大小：771 K
• 卷排序：449

文摘

The aim of this paper is to study a concentration-compactness principle for homogeneous fractional Sobolev space Ds,2(RN)Ds,2(RN) for 0<s<min⁡{1,N/2}0<s<min⁡{1,N/2}. As an application we establish Palais–Smale compactness for the Lagrangian associated to the fractional scalar field equation (−Δ)su=f(x,u)(−Δ)su=f(x,u) for 0<s<10<s<1. Moreover, using an analytic framework based on Ds,2(RN)Ds,2(RN), we obtain the existence of ground state solutions for a wide class of nonlinearities in the critical growth range.