Publication details
Quasilinear Schrödinger equations with Stein-Weiss type convolution and critical exponential nonlinearity in R^N
| Authors | |
|---|---|
| Year of publication | 2024 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Geometric Analysis |
| MU Faculty or unit | |
| Citation | |
| Web | https://link.springer.com/article/10.1007/s12220-023-01505-5 |
| Doi | http://dx.doi.org/10.1007/s12220-023-01505-5 |
| Keywords | Quasilinear Schrödinger equation; N-Laplacian; Stein-Weiss type convolution; Trudinger-Moser inequality; Critical exponent |
| Description | In this article, we investigate the existence of the positive solutions to the following class of quasilinear {Schr\"odinger} equations involving Stein-Weiss type convolution \begin{align*} -\Delta_N u -\Delta_N (u^{2})u +V(x)|u|^{N-2}u= \left(\int_{\mathbb R^N}\frac{F(y,u)}{|y|^\beta|x-y|^{\mu}}~dy\right)\frac{f(x,u)}{|x|^\beta} \;\; \text{ in}\; \mathbb R^N, \end{align*} where $N\geq 2,\,$ $0<\mu<N,\, \beta\geq 0,$ and $2\beta+\mu\leq N.$ The potential $V:\mathbb R^N\to \mathbb R$ is a continuous function satisfying $0<V_0\leq V(x)$ for all $x\in \mathbb R^N$ and some appropriate assumptions. The nonlinearity $f:\mathbb R^N\times \mathbb R\to \mathbb R$ is a continuous function with critical exponential growth in the sense of the Trudinger-Moser inequality and $F(x,s)=\int_{0}^s f(x,t)dt$ is the primitive of $f$. |