Least Energy Solutions with Sign Information for Parametric Double Phase Problems

We consider a parametric double phase Dirichlet problem. In the reaction there is superlinear perturbation term which satisfies weak Nehari-type monotonicity condition. Using Nehari manifold method, we show that for all parameters below critical value, problem has at least three nontrivial solutions with sign information. The parameter value precisely identified in terms of spectrum lower exponent part differential operator.