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@article{2367057, author = {Biswas, Reshmi and Goyal, Sarika and Sreenadh, K.}, article_number = {2}, 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}, language = {eng}, issn = {1050-6926}, journal = {Journal of Geometric Analysis}, title = {Quasilinear Schrödinger equations with Stein-Weiss type convolution and critical exponential nonlinearity in R^N}, url = {https://link.springer.com/article/10.1007/s12220-023-01505-5}, volume = {34}, year = {2024} }
TY - JOUR ID - 2367057 AU - Biswas, Reshmi - Goyal, Sarika - Sreenadh, K. PY - 2024 TI - Quasilinear Schrödinger equations with Stein-Weiss type convolution and critical exponential nonlinearity in R^N JF - Journal of Geometric Analysis VL - 34 IS - 2 SP - 1-52 EP - 1-52 PB - Springer SN - 10506926 KW - Quasilinear Schrödinger equation KW - N-Laplacian KW - Stein-Weiss type convolution KW - Trudinger-Moser inequality KW - Critical exponent UR - https://link.springer.com/article/10.1007/s12220-023-01505-5 N2 - 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 $f$. ER -
BISWAS, Reshmi, Sarika GOYAL a K. SREENADH. Quasilinear Schrödinger equations with Stein-Weiss type convolution and critical exponential nonlinearity in R\^{}N. \textit{Journal of Geometric Analysis}. Springer, 2024, roč.~34, č.~2, s.~1-52. ISSN~1050-6926. Dostupné z: https://dx.doi.org/10.1007/s12220-023-01505-5.
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