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.

中文翻译：

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p（x）-Laplace型多调和方程的无穷多个解

我们通过不带（AR）条件的山pass原理显示了一类拟线性椭圆p（x）-多调和Kirchhoff方程的无穷弱解的存在。此外，我们在克拉米诺条件下，根据Krasnoselskii引入的属论和抽象临界点定理（Ljusternik-Schnirelman理论的变体）引入了该方程的无穷多个解。