# Existence of Positive Solutions for a class of Quasilinear Schr\"{o}dinger Equations of Choquard type

## TL;DR

This paper proves the existence of positive solutions for a class of quasilinear Schrödinger equations of Choquard type involving Riesz potentials, under certain conditions on the potential function V(x).

## Contribution

It establishes the existence of positive solutions for a specific class of quasilinear Schrödinger equations with nonlocal Choquard terms, extending previous results to more general conditions.

## Key findings

- Existence of positive solutions under specified conditions on V(x).
- Extension of solution existence results to quasilinear Schrödinger equations with Choquard nonlinearity.
- Applicable for a range of p values satisfying certain inequalities.

## Abstract

In this paper, we study the following quasilinear Schr\"{o}dinger equation of Choquard type $$ -\triangle u+V(x)u-\triangle (u^{2})u=(I_\alpha *|u|^p)|u|^{p-2}u, \ \ x \in \mathbb{R}^{N}, $$ where $N\geq 3$,\ $0<\alpha<N$, $\frac{2(N+\alpha)}{N}\leq p<\frac{2(N+\alpha)}{N-2}$ and $I_\alpha$ is a Riesz potential. Under appropriate assumptions on $V(x)$, we establish the existence of positive solutions.