We consider a nonlinear Dirichlet problem driven by a (p, q)-Laplace differential operator (1 < q < p). The reaction is (p − 1)-linear near ±∞ and the problem is noncoercive. Using variational tools and truncation and comparison techniques together with critical groups, we produce five nontrivial smooth solutions all with sign information and ordered. In the particular case when q = 2, we produce a second nodal solution for a total of six nontrivial smooth solutions all with sign information.

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关于非强制性 (p, q)-方程

我们考虑由 ( p, q )-拉普拉斯微分算子 (1 < q < p )驱动的非线性狄利克雷问题。反应是 ( p − 1) 线性接近 ±∞ 并且问题是非强制性的。使用变分工具、截断和比较技术以及关键组，我们产生了五个非平凡的平滑解决方案，所有解决方案都带有符号信息并有序。在q = 2的特殊情况下，我们为总共六个非平凡的平滑解产生第二个节点解，所有解都带有符号信息。