We consider a double phase problem driven by the sum of the ▫$p$▫-Laplace operator and a weighted ▫$q$▫-Laplacian ▫$(q<p)$▫, with a weight function which is not bounded away from zero. The reaction ...term is ▫$(p-1)$▫-superlinear. Employing the Nehari method, we show that the equation has a ground state solution of constant sign and a nodal (sign-changing) solution.
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