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In this paper we introduce a new double phase Baouendi-Grushin type operatorwith variable coefficients. We give basic properties of the correspondingfunctions space and prove a compactness result. In the second part, usingtopological argument, we prove the existence of weak solutions of somenonvariational problems in which this new operator is present. The presentpaper extends and complements some of our previous contributions related todouble phase anisotropic variational integrals.

Nonvariational and singular double phase problems for the Baouendi-Grushin operator