标题： 关于拟线性椭圆型局部和非局部方程及系统具有 Pohozaev 型恒等式的类，及其应用 显示英文标题

标题： Pohozaev-type identities for classes of quasilinear elliptic local and nonlocal equations and systems, with applications

摘要： 本文中，我们建立了拟线性椭圆方程和系统的一类Pohozaev型恒等式，涉及局部和非局部的$p$-Laplace 算子。 具体来说，我们在$\mathbb{R}^n$中得到了纯各向异性$p$-Laplace 方程、纯分数阶$p$-Laplace 方程以及同时具有各向异性和分数阶$p$-Laplace 特性的方程的这些恒等式。 我们也将这些结果推广到相应的系统中。 据我们所知，即使在$p=2$的混合情形下，我们导出的恒等式也是新的。 最后，我们展示了我们的主要结果的一些应用。 显示英文摘要

摘要： In this article, we establish Pohozaev-type identities for a class of quasilinear elliptic equations and systems involving both local and nonlocal $p$-Laplace operators. Specifically, we obtain these identities in $\mathbb{R}^n$ for the purely anisotropic $p$-Laplace equations, the purely fractional $p$-Laplace equations, as well as for equations that incorporate both anisotropic and fractional $p$-Laplace features. We also extend these results to the corresponding systems. To the best of our knowledge, the identities we derive in the mixed case are new even when $p=2$. Finally, we illustrate some of the applications of our main results.