Non-Degeneracy and Infinitely Many Solutions for Critical SchrÖDinger-Maxwell Type Problem

Yuxia Guo; Yichen Hu; Shaolong Peng

doi:10.1007/s11118-024-10123-x

Non-Degeneracy and Infinitely Many Solutions for Critical SchrÖDinger-Maxwell Type Problem

Yuxia Guo
, Yichen Hu
, Shaolong Peng^*

^*Corresponding author for this work

Tsinghua University
CAS - Academy of Mathematics and System Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we consider the following Schrödinger-Maxwell type equation with critical exponent -Δu=K(y)(1|x|^n-2∗K(x)|u|^{ⁿ⁺²^n-2})u^{⁴^n-2},inRⁿ,(0.1) where the function K satisfies the assumption F, and ∗ stands for the standard convolution. We first derived the non-degeneracy result for the critical Schrödinger-Maxwell equation. Then, as an application, we proved that problem Eq. (0.1) admits infinitely many non-radial positive solutions with arbitrary large energy. We believe that the various new ideas and technique computations that we used in this paper would be useful to deal with other related elliptic problems involving convolution nonlinear terms.

Original language	English
Pages (from-to)	625-658
Number of pages	34
Journal	Potential Analysis
Volume	61
Issue number	4
DOIs	https://doi.org/10.1007/s11118-024-10123-x
State	Published - Dec 2024
Externally published	Yes

Keywords

35B33
35J60
Finite Reduction method
Infinitely many solutions
Non-degeneracy
Primary: 35J20
Schrödinger-Maxwell equation
Secondary: 35A15

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10.1007/s11118-024-10123-x

Cite this

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title = "Non-Degeneracy and Infinitely Many Solutions for Critical Schr{\"O}Dinger-Maxwell Type Problem",

abstract = "In this paper, we consider the following Schr{\"o}dinger-Maxwell type equation with critical exponent -Δu=K(y)(1|x|n-2∗K(x)|u|n+2n-2)u4n-2,inRn,(0.1) where the function K satisfies the assumption F, and ∗ stands for the standard convolution. We first derived the non-degeneracy result for the critical Schr{\"o}dinger-Maxwell equation. Then, as an application, we proved that problem Eq. (0.1) admits infinitely many non-radial positive solutions with arbitrary large energy. We believe that the various new ideas and technique computations that we used in this paper would be useful to deal with other related elliptic problems involving convolution nonlinear terms.",

keywords = "35B33, 35J60, Finite Reduction method, Infinitely many solutions, Non-degeneracy, Primary: 35J20, Schr{\"o}dinger-Maxwell equation, Secondary: 35A15",

author = "Yuxia Guo and Yichen Hu and Shaolong Peng",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Nature B.V. 2024.",

year = "2024",

month = dec,

doi = "10.1007/s11118-024-10123-x",

language = "英语",

volume = "61",

pages = "625--658",

journal = "Potential Analysis",

issn = "0926-2601",

publisher = "Springer Netherlands",

number = "4",

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TY - JOUR

T1 - Non-Degeneracy and Infinitely Many Solutions for Critical SchrÖDinger-Maxwell Type Problem

AU - Guo, Yuxia

AU - Hu, Yichen

AU - Peng, Shaolong

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Nature B.V. 2024.

PY - 2024/12

Y1 - 2024/12

N2 - In this paper, we consider the following Schrödinger-Maxwell type equation with critical exponent -Δu=K(y)(1|x|n-2∗K(x)|u|n+2n-2)u4n-2,inRn,(0.1) where the function K satisfies the assumption F, and ∗ stands for the standard convolution. We first derived the non-degeneracy result for the critical Schrödinger-Maxwell equation. Then, as an application, we proved that problem Eq. (0.1) admits infinitely many non-radial positive solutions with arbitrary large energy. We believe that the various new ideas and technique computations that we used in this paper would be useful to deal with other related elliptic problems involving convolution nonlinear terms.

AB - In this paper, we consider the following Schrödinger-Maxwell type equation with critical exponent -Δu=K(y)(1|x|n-2∗K(x)|u|n+2n-2)u4n-2,inRn,(0.1) where the function K satisfies the assumption F, and ∗ stands for the standard convolution. We first derived the non-degeneracy result for the critical Schrödinger-Maxwell equation. Then, as an application, we proved that problem Eq. (0.1) admits infinitely many non-radial positive solutions with arbitrary large energy. We believe that the various new ideas and technique computations that we used in this paper would be useful to deal with other related elliptic problems involving convolution nonlinear terms.

KW - 35B33

KW - 35J60

KW - Finite Reduction method

KW - Infinitely many solutions

KW - Non-degeneracy

KW - Primary: 35J20

KW - Schrödinger-Maxwell equation

KW - Secondary: 35A15

UR - https://www.scopus.com/pages/publications/85183040243

U2 - 10.1007/s11118-024-10123-x

DO - 10.1007/s11118-024-10123-x

M3 - 文章

AN - SCOPUS:85183040243

SN - 0926-2601

VL - 61

SP - 625

EP - 658

JO - Potential Analysis

JF - Potential Analysis

IS - 4

ER -

Non-Degeneracy and Infinitely Many Solutions for Critical SchrÖDinger-Maxwell Type Problem

Abstract

Keywords

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