The concentration-compactness principles for Ws,p(·,·)(ℝN) and application

Abstract

We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical nonlocal problems with variable exponents, which is even new for constant exponent case.

Keywords

• fractional p-laplacian
• p(·)-laplacian
• fractional sobolev spaces with variable exponents
• critical imbedding
• concentration-compactness principles
• variational methods
• 35b33
• 35d30
• 35j20
• 35r11
• 46e35
• 49j35