# A study and an application of the concentration compactness type principle

@article{Panda2019ASA, title={A study and an application of the concentration compactness type principle}, author={Akasmika Panda and Debajyoti Choudhuri}, journal={arXiv: Analysis of PDEs}, year={2019} }

In this article we develop a concentration compactness type principle in a variable exponent setup. As an application of this principle we discuss a problem involving fractional `{\it $(p(x),p^+)$-Laplacian}' and power nonlinearities with exponents $(p^+)^*$, $p_s^*(x)$ with the assumption that the critical set $\{x\in\Omega:p_s^*(x)=(p^+)^*\}$ is nonempty.

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