拟线性Schrödinger方程的解:亚临界和临界情况

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-05-01 DOI:10.1063/5.0142706

Gelson C. G. dos Santos, Laila C. Fontinele, Rubia G. Nascimentoa, Suellen Cristina Q. Arrudab

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引用次数: 0

摘要

本文建立了具有亚临界和临界增长的非线性拟线性Schrödinger方程驻波解的存在性。为了应用变分方法并规避问题的“缺乏紧性”，我们结合了Colin-Jeanjean[非线性学报，56,213-226 (2004)]，fangsszulkin [J]。是不同的。方程，254,2015-2032(2013)].刘旺旺。是不同的。方程187,473-493(2003)]与Del Pino-Felmer的惩罚技术[c. Var. Partial Differ.]方程4,121 - 137 (1996)]，Moser的迭代法，以及对Alves论证的适应[J]。椭圆Parabol。方程1,231 - 241(2015)]的半线性情况。

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Solutions for a quasilinear Schrödinger equation: Subcritical and critical cases

In this paper, we establish the existence of standing wave solutions for quasilinear Schrödinger equations involving nonlinearity with subcritical and critical growth. To apply the variational method and circumvent the “lack of compactness” of the problem, we combine the dual approach developed by Colin–Jeanjean [Nonlinear Anal. 56, 213–226 (2004)], Fang–Szulkin [J. Differ. Equations, 254, 2015–2032 (2013)], and Liu–Wang–Wang [J. Differ. Equations 187, 473–493 (2003)] with Del Pino–Felmer’s penalization technique [Calc. Var. Partial Differ. Equations 4, 121–137 (1996)], Moser’s iteration method, and an adaptation of Alves’ arguments [J. Elliptic Parabol. Equations 1, 231–241 (2015)] of the semilinear case.

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来源期刊

Journal of Mathematical Physics Analysis Geometry PHYSICS, MATHEMATICAL-

CiteScore

0.70

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Mathematical Physics, Analysis, Geometry (JMPAG) publishes original papers and reviews on the main subjects: mathematical problems of modern physics; complex analysis and its applications; asymptotic problems of differential equations; spectral theory including inverse problems and their applications; geometry in large and differential geometry; functional analysis, theory of representations, and operator algebras including ergodic theory. The Journal aims at a broad readership of actively involved in scientific research and/or teaching at all levels scientists.