Localized nodal solutions for semiclassical quasilinear Choquard equations with subcritical growth

In this article, we study the existence of localized nodal solutions for semiclassical quasilinear Choquard equations with subcritical growth $$-\varepsilon^p \Delta_{p} v +V(x)|v|^{p-2}v = \varepsilon^{\alpha-N} |v|^{q-2}v \int_{\mathbb{R}^N} \frac{|v(y)|^q}{|x-y|^{\alpha}}\,dy ,\quad x \in \mathbb{R}^N\,, $$ where \(N\geq 3\), \(1<p<N\), \(0<\alpha <\min\{2p,N-1\}\), \(p<q<p_\alpha^*\), \(p_\alpha^*= \frac{p(2N-\alpha)}{2(N-p)}\), \(V\) is a bounded function. By the perturbation method and the method of invariant sets of descending flow, for small \(\varepsilon\) we establish the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function \(V\).