Abstract
We show the existence of infinitely many weak solutions to a class of quasilinear elliptic p(x)‐polyharmonic Kirchhoff equations via the mountain pass principle without the (AR) condition. Furthermore, we obtain infinitely many solutions to this equation based on the genus theory, introduced by Krasnoselskii and the abstract critical point theorem (a variant of Ljusternik‐Schnirelman theory) under Cerami condition.
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