The concentration-compactness principle for Musielak-Orlicz spaces and applications

Abstract: This paper extends the Concentration-Compactness Principle to Musielak-Orlicz spaces, working in both bounded and unbounded domains. We show that our results include important special cases like classical Orlicz spaces, variable exponent spaces, double phase spaces, and a new type of double phase problem where the exponents depend on the solution. Using these general results with variational methods, we prove that certain quasilinear equations with critical nonlinear terms have solutions.