Multiple solutions with sign information for double‐phase problems with unbalanced growth

Abstract We consider a double‐phase Dirichlet problem with unbalanced growth and a reaction term which is ‐sublinear and has partial interaction with the first eigenvalue of the weighted differential operator (nonuniform nonresonance). Using the Nehari method, we show that the problem has at least three nontrivial bounded solutions, positive, negative and nodal (sign‐changing). This paper extends and complements the main results in the recent paper Papageorgiou–Pudelko–Rădulescu ( Math. Annalen 385 (2023) 1707–1745).