Classification of solutions to some elliptic equations with Robin boundary condition and finite Morse index

被引：0

作者：

Rebhi, Salem ^{[1
]}

Ghabi, Khouloud ^{[1
]}

机构：

[1] Univ Tunis El Manar, Fac Sci Tunis, Dept Math, Campus Univ, Tunis 2092, Tunisia

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2025年 / 542卷 / 02期

关键词：

Liouville type theorems; Stable solutions; Morse index; Robin boundary condition;

D O I：

10.1016/j.jmaa.2024.128790

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We deal here with the non-existence of weak finite Morse index solutions to the following nonlinear elliptic equation -Delta u=(1+|x|(alpha))|u|(p-1)u in R-N, or in half space with Robin boundary condition, where N >= 2, alpha > -2 and p >1. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页数：15

共 19 条

[1] SOLUTIONS OF SUPERLINEAR ELLIPTIC-EQUATIONS AND THEIR MORSE INDEXES
BAHRI, A
LIONS, PL
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1992, 45 (09) : 1205 - 1215
[2] MORSE INDEX OF SOME MIN MAX CRITICAL-POINTS .1. APPLICATION TO MULTIPLICITY RESULTS
BAHRI, A
LIONS, PL
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1988, 41 (08) : 1027 - 1037
[3] Bahri A., 1986, SEM EQ DER PART EC P
[4] Finite Morse index solutions of an elliptic equation with supercritical exponent
Dancer, E. N.
Du, Yihong
Guo, Zongming
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 250 (08) : 3281 - 3310
[5] Partial regularity of finite Morse index solutions to the Lane-Emden equation
Davila, Juan
Dupaigne, Louis
Farina, Alberto
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2011, 261 (01) : 218 - 232
[6] On a semilinear elliptic problem without (PS) condition
de Figueiredo, DG
Yang, J
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 187 (02) : 412 - 428
[7] PATTERN-FORMATION IN GENERALIZED TURING SYSTEMS .1. STEADY-STATE PATTERNS IN SYSTEMS WITH MIXED BOUNDARY-CONDITIONS
DILLON, R
MAINI, PK
OTHMER, HG
[J]. JOURNAL OF MATHEMATICAL BIOLOGY, 1994, 32 (04) : 345 - 393
[8] On the classification of solutions of the Lane-Emden equation on unbounded domains of RN
Farina, Alberto
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2007, 87 (05): : 537 - 561
[9] Classification of Finite Morse Index Solutions for Robin Boundary Value Problems
Ghabi, Khouloud
[J]. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2023, 29 (04) : 1175 - 1185
[10] Solutions of superlinear elliptic equations and their Morse indices, II
Harrabi, A
Rebhi, S
Selmi, A
[J]. DUKE MATHEMATICAL JOURNAL, 1998, 94 (01) : 159 - 179

← 1 2 →