The concentration-compactness principles for W ^{<i>s,p</i> (·,·)} (ℝ <i> ^N </i> ) and application

Abstract

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.