Infinitely many sign-changing normalized solutions of competition-diffusion p-Laplacian systems

In this paper, under normalized constraints, we apply the vector genus and descending flow method to establish infinitely many sign-changing solutions for the system of m p-Laplacian Schrödinger equations with competition interactions

$ \begin{cases} -\Delta_p u_i+ \mu_i g_i(u_i) +\beta f_i(u_i) \sum\nolimits_{j\neq i} F_j(u_j) = \lambda_{i} |u_i|^{p-2}u_i, \\ \int_\Omega |u_i|^p \mathrm{d}x = 1, u_i\in W_{0}^{1, p}(\Omega), i = 1, 2, \cdots, m, \end{cases} $

where $ \Omega $ is a bounded regular domain in $ {\mathbb{R}}^N (N\geq 2) $, $ \beta > 0 \, and \, \mu_i\geq 0 $ are prescribed parameters, $ f_i\, and \, g_i $ are odd functions satisfying some growth conditions, and $ F_i(t) = \int_0^t f_i(\xi)\mathrm{d}\xi $. The innovation is that we construct a tangent pseudo-gradient vector field for the energy functional on the constrained manifold, which can be used to find invariant sets of descending flow. The difficulty is reinforced by the p-Laplacian operator, and also by the normalized constraint. Since we are dealing with $ p>1 $ in a unified way, the energy functional may be not regular enough and the p-Laplacian operator is not linear, so we cannot benefit from certain classical techniques directly.