Quasilinear Schrödinger equations with Stein-Weiss type convolution and critical exponential nonlinearity in R^N

BISWAS, Reshmi, Sarika GOYAL and K. SREENADH. Quasilinear Schrödinger equations with Stein-Weiss type convolution and critical exponential nonlinearity in R^N. Journal of Geometric Analysis. Springer, 2024, vol. 34, No 2, p. 1-52. ISSN 1050-6926. Available from: https://dx.doi.org/10.1007/s12220-023-01505-5.

Basic information

• Original name: Quasilinear Schrödinger equations with Stein-Weiss type convolution and critical exponential nonlinearity in R^N
• Authors: BISWAS, Reshmi (356 India, belonging to the institution), Sarika GOYAL and K. SREENADH (guarantor).
• Edition: Journal of Geometric Analysis, Springer, 2024, 1050-6926.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: United States of America
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• Impact factor: Impact factor: 1.100 in 2022
• Organization unit: Faculty of Science
• Doi: http://dx.doi.org/10.1007/s12220-023-01505-5
• UT WoS: 001134164400002
• Keywords in English: Quasilinear Schrödinger equation; N-Laplacian; Stein-Weiss type convolution; Trudinger-Moser inequality; Critical exponent
• Tags: rivok
• Tags: International impact, Reviewed

Abstract

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 $f$.