Concentration solutions to the singularly prescribed Gaussian and geodesic curvatures problem

Liping Wang; Chunyi Zhao

doi:10.1016/j.jde.2021.08.023

Concentration solutions to the singularly prescribed Gaussian and geodesic curvatures problem

Liping Wang
, Chunyi Zhao^*

^*此作品的通讯作者

数学科学学院

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

We consider the following Liouville-type equation with exponential Neumann boundary condition: [Formula presented] where D⊂R² is the unit disk, ε²K(x)>0 and εκ(x)>0 stand for the prescribed Gaussian curvature and geodesic curvature of the boundary, respectively. We prove the existence of concentration solutions if κ(x)+K(x)+κ(x)² (x∈∂D) has a local extremum point, which is a new result for exponential Neumann boundary problems.

源语言	英语
页（从-至）	266-299
页数	34
期刊	Journal of Differential Equations
卷	301
DOI	https://doi.org/10.1016/j.jde.2021.08.023
出版状态	已出版 - 15 11月 2021

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abstract = "We consider the following Liouville-type equation with exponential Neumann boundary condition: [Formula presented] where D⊂R2 is the unit disk, ε2K(x)>0 and εκ(x)>0 stand for the prescribed Gaussian curvature and geodesic curvature of the boundary, respectively. We prove the existence of concentration solutions if κ(x)+K(x)+κ(x)2 (x∈∂D) has a local extremum point, which is a new result for exponential Neumann boundary problems.",

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author = "Liping Wang and Chunyi Zhao",

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AU - Wang, Liping

AU - Zhao, Chunyi

PY - 2021/11/15

Y1 - 2021/11/15

N2 - We consider the following Liouville-type equation with exponential Neumann boundary condition: [Formula presented] where D⊂R2 is the unit disk, ε2K(x)>0 and εκ(x)>0 stand for the prescribed Gaussian curvature and geodesic curvature of the boundary, respectively. We prove the existence of concentration solutions if κ(x)+K(x)+κ(x)2 (x∈∂D) has a local extremum point, which is a new result for exponential Neumann boundary problems.

AB - We consider the following Liouville-type equation with exponential Neumann boundary condition: [Formula presented] where D⊂R2 is the unit disk, ε2K(x)>0 and εκ(x)>0 stand for the prescribed Gaussian curvature and geodesic curvature of the boundary, respectively. We prove the existence of concentration solutions if κ(x)+K(x)+κ(x)2 (x∈∂D) has a local extremum point, which is a new result for exponential Neumann boundary problems.

KW - Concentration

KW - Existence

KW - Exponential Neumann boundary condition

UR - https://www.scopus.com/pages/publications/85114012701

U2 - 10.1016/j.jde.2021.08.023

DO - 10.1016/j.jde.2021.08.023

M3 - 文章

AN - SCOPUS:85114012701

SN - 0022-0396

VL - 301

SP - 266

EP - 299

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Concentration solutions to the singularly prescribed Gaussian and geodesic curvatures problem

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