Classification of solutions to Finsler <inline-formula><tex-math id="M1">$ p $</tex-math></inline-formula>-Laplacian equation

In this paper, we consider the following problem$ \begin{equation} \Delta^H_p u + f(u) = 0, \end{equation} $for $ f $ nonnegative and with subcritical exponents in $ \mathbb{R}^n $ and $ \mathbb{R}^n_+ $. Based on some delicate integral identities and the method of moving planes, we have settled down the classification of nonnegative solutions for (1) in $ \mathbb{R}^n $ and $ \mathbb{R}^n_+ $ with $ 1 < p < n $. Our result can be seen as a counterpart in the subcritical case of the classification results in [17] for critical Finsler $ p $-Laplacian equations.