The Henon problem with large exponent in the disc

被引：13

作者：

Amadori, Anna Lisa ^{[1
]}

Gladiali, Francesca ^{[2
]}

机构：

[1] Univ Napoli Parthenope, Dipartimento Sci Applicate, Ctr Direz Napoli, Isola C4, I-80143 Naples, Italy

[2] Univ Sassari, Dipartimento Chim & Farm, Via Piandanna 4, I-07100 Sassari, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2020年 / 268卷 / 10期

关键词：

Nodal solutions; Concentration phenomena; Morse index; Least energy radial and non-radial solutions; 2-DIMENSIONAL ELLIPTIC PROBLEM; LANE-EMDEN PROBLEMS; NODAL SOLUTIONS; RADIAL SOLUTIONS; SYMMETRY; UNIQUENESS; EQUATIONS;

D O I：

10.1016/j.jde.2019.11.017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we consider the Henon problem in the unit disc with Dirichlet boundary conditions. We study the asymptotic profile of least energy and nodal least energy radial solutions and then deduce the exact computation of their Morse index for large values of the exponent p. As a consequence of this computation a multiplicity result for positive and nodal solutions is obtained. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：5892 / 5944

页数：53

共 50 条

[1] CONCENTRATING SOLUTIONS FOR AN ANISOTROPIC PLANAR ELLIPTIC NEUMANN PROBLEM WITH HARDY-HENON WEIGHT AND LARGE EXPONENT
Zhang, Yibin
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2022, 60 (01) : 33 - 97
[2] A Note on Nonradial Nodal Solutions to the Henon Problem in the Disc
Gladiali, Francesca
Stegel, Giovanni
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2022, 71 (02) : 715 - 733
[3] The maximum Lyapunov exponent of the chaotic motion in the Henon-Heiles problem
Melnikov, AV
Shevchenko, II
ORDER AND CHAOS IN STELLAR AND PLANETARY SYSTEMS, 2004, 316 : 34 - 36
[4] New type solutions for a biharmonic Henon problem with slightly subcritical Sobolev exponent
Chen, Wenjing
Yu, Fang
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2025, 549 (01)
[5] SOME RESULTS ON TWO-DIMENSIONAL HENON EQUATION WITH LARGE EXPONENT IN NONLINEARITY
Zhao, Chunyi
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2013, 12 (02) : 803 - 813
[6] Asymptotic behavior on the Henon equation with supercritical exponent
Li ShuJuan
Peng ShuangJie
SCIENCE IN CHINA SERIES A-MATHEMATICS, 2009, 52 (10): : 2185 - 2194
[7] ON THE NUMBER OF MAXIMUM POINTS OF LEAST ENERGY SOLUTION TO A TWO-DIMENSIONAL HENON EQUATION WITH LARGE EXPONENT
Takahashi, Futoshi
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2013, 12 (03) : 1237 - 1241
[8] A critical exponent for Henon type equation on the hyperbolic space
Hasegawa, Shoichi
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 129 : 343 - 370
[9] CONCENTRATING SOLUTIONS FOR AN ANISOTROPIC ELLIPTIC PROBLEM WITH LARGE EXPONENT
Wang, Liping
Ye, Dong
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2015, 35 (08) : 3771 - 3797
[10] THE HENON EQUATION WITH A CRITICAL EXPONENT UNDER THE NEUMANN BOUNDARY CONDITION
Byeon, Jaeyoung
Jin, Sangdon
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2018, 38 (09) : 4353 - 4390

← 1 2 3 4 5 →