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Using variational methods, we obtain several multiplicity results for doublephase problems that involve variable exponents and a new type of criticalgrowth. This new critical growth is better suited for double phase problemswhen compared to previous works on the subject. In order to overcome the lackof compactness caused by the critical exponents, we establish aconcentration-compactness principle of Lions type for spaces associated withdouble phase operators, which is of independent interest to us. Our results arenew, even in the case of constant exponents.

Multiplicity results for double phase problems involving a new type of critical growth