Eigenvalues for double phase variational problems

We study an eigenvalue problem in the framework of double phase variational\r\nintegrals, and we introduce a sequence of nonlinear eigenvalues by a minimax procedure. We\r\nestablish a continuity result for the nonlinear eigenvalues with respect to the variations of the\r\nphases. Furthermore, we investigate the growth rate of this sequence and get a Weyl-type law\r\nconsistent with the classical law for the p-Laplacian operator when the two phases agree.