AIMS Mathematics | |
Standing waves for quasilinear Schrödinger equations involving double exponential growth | |
article | |
Yony Raúl Santaria Leuyacc1  | |
[1] Faculty of Mathematical Sciences, National University of San Marcos | |
关键词: quasilinear Schrödinger equation; double exponential growth; mountain pass theorem; Trudinger-Moser inequality; dual approach; | |
DOI : 10.3934/math.2023086 | |
学科分类:地球科学(综合) | |
来源: AIMS Press | |
【 摘 要 】
We will focus on the existence of nontrivial, nonnegative solutions to the following quasilinear Schrödinger equation$ \begin{equation*} \left\lbrace\begin{array}{rcll} -{\rm div} \Big(\log \dfrac{e}{|x|}\nabla u\Big) -{\rm div} \Big(\log \dfrac{e}{|x|}\nabla (u^2)\Big) u \ & = &\ g(x, u), &\ x \in B_1, \\ u \ & = &\ 0, &\ x \in \partial B_1, \end{array}\right. \end{equation*} $where $ B_1 $ denotes the unit ball centered at the origin in $ \mathbb{R}^2 $ and $ g $ behaves like $ {\rm exp}(e^{s^4}) $ as $ s $ tends to infinity, the growth of the nonlinearity is motivated by a Trudinder-Moser inequality version, which admits double exponential growth. The proof involves a change of variable (a dual approach) combined with the mountain pass theorem.
【 授权许可】
CC BY
【 预 览 】
Files | Size | Format | View |
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RO202302200002453ZK.pdf | 246KB | download |