American Institute of Mathematical Sciences

Advanced
July  2005, 12(4): 737-746. doi: 10.3934/dcds.2005.12.737

Multiple sign-changing solutions of an elliptic eigenvalue problem

Aixia Qian 1, and  Shujie Li 2,

1. 

Department of Mathematics, Qufu Normal University, Qufu Shangdong, 273165, China
2. 

Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080

Received  December 2003 Revised  October 2004 Published  January 2005

We prove the existences of multiple sign-changing solutions for a semilinear elliptic eigenvalue problem with constraint by using variational methods under weaker conditions.
Keywords: Minimax theory, sign-changing solution, elliptic eigenvalue problems..
Mathematics Subject Classification: Primary: 35J25, 85E0.
Citation: Aixia Qian, Shujie Li. Multiple sign-changing solutions of an elliptic eigenvalue problem. Discrete and Continuous Dynamical Systems, 2005, 12 (4) : 737-746. doi: 10.3934/dcds.2005.12.737
[1]

Salomón Alarcón, Jinggang Tan. Sign-changing solutions for some nonhomogeneous nonlocal critical elliptic problems. Discrete and Continuous Dynamical Systems, 2019, 39 (10) : 5825-5846. doi: 10.3934/dcds.2019256
[2]

Gabriele Cora, Alessandro Iacopetti. Sign-changing bubble-tower solutions to fractional semilinear elliptic problems. Discrete and Continuous Dynamical Systems, 2019, 39 (10) : 6149-6173. doi: 10.3934/dcds.2019268
[3]

Yanfang Peng, Jing Yang. Sign-changing solutions to elliptic problems with two critical Sobolev-Hardy exponents. Communications on Pure and Applied Analysis, 2015, 14 (2) : 439-455. doi: 10.3934/cpaa.2015.14.439
[4]

Zhengping Wang, Huan-Song Zhou. Radial sign-changing solution for fractional Schrödinger equation. Discrete and Continuous Dynamical Systems, 2016, 36 (1) : 499-508. doi: 10.3934/dcds.2016.36.499
[5]

Yohei Sato, Zhi-Qiang Wang. On the least energy sign-changing solutions for a nonlinear elliptic system. Discrete and Continuous Dynamical Systems, 2015, 35 (5) : 2151-2164. doi: 10.3934/dcds.2015.35.2151
[6]

Teodora-Liliana Dinu. Entire solutions of the nonlinear eigenvalue logistic problem with sign-changing potential and absorption. Communications on Pure and Applied Analysis, 2003, 2 (3) : 311-321. doi: 10.3934/cpaa.2003.2.311
[7]

Yuanxiao Li, Ming Mei, Kaijun Zhang. Existence of multiple nontrivial solutions for a $p$-Kirchhoff type elliptic problem involving sign-changing weight functions. Discrete and Continuous Dynamical Systems - B, 2016, 21 (3) : 883-908. doi: 10.3934/dcdsb.2016.21.883
[8]

Jun Yang, Yaotian Shen. Weighted Sobolev-Hardy spaces and sign-changing solutions of degenerate elliptic equation. Communications on Pure and Applied Analysis, 2013, 12 (6) : 2565-2575. doi: 10.3934/cpaa.2013.12.2565
[9]

Wen Zhang, Xianhua Tang, Bitao Cheng, Jian Zhang. Sign-changing solutions for fourth order elliptic equations with Kirchhoff-type. Communications on Pure and Applied Analysis, 2016, 15 (6) : 2161-2177. doi: 10.3934/cpaa.2016032
[10]

Huxiao Luo, Xianhua Tang, Zu Gao. Sign-changing solutions for non-local elliptic equations with asymptotically linear term. Communications on Pure and Applied Analysis, 2018, 17 (3) : 1147-1159. doi: 10.3934/cpaa.2018055
[11]

Tsung-Fang Wu. On semilinear elliptic equations involving critical Sobolev exponents and sign-changing weight function. Communications on Pure and Applied Analysis, 2008, 7 (2) : 383-405. doi: 10.3934/cpaa.2008.7.383
[12]

Jie Yang, Haibo Chen. Multiplicity and concentration of positive solutions to the fractional Kirchhoff type problems involving sign-changing weight functions. Communications on Pure and Applied Analysis, 2021, 20 (9) : 3065-3092. doi: 10.3934/cpaa.2021096
[13]

Mateus Balbino Guimarães, Rodrigo da Silva Rodrigues. Elliptic equations involving linear and superlinear terms and critical Caffarelli-Kohn-Nirenberg exponent with sign-changing weight functions. Communications on Pure and Applied Analysis, 2013, 12 (6) : 2697-2713. doi: 10.3934/cpaa.2013.12.2697
[14]

M. Ben Ayed, Kamal Ould Bouh. Nonexistence results of sign-changing solutions to a supercritical nonlinear problem. Communications on Pure and Applied Analysis, 2008, 7 (5) : 1057-1075. doi: 10.3934/cpaa.2008.7.1057
[15]

Hui Guo, Tao Wang. A note on sign-changing solutions for the Schrödinger Poisson system. Electronic Research Archive, 2020, 28 (1) : 195-203. doi: 10.3934/era.2020013
[16]

Guirong Liu, Yuanwei Qi. Sign-changing solutions of a quasilinear heat equation with a source term. Discrete and Continuous Dynamical Systems - B, 2013, 18 (5) : 1389-1414. doi: 10.3934/dcdsb.2013.18.1389
[17]

Jiaquan Liu, Xiangqing Liu, Zhi-Qiang Wang. Sign-changing solutions for a parameter-dependent quasilinear equation. Discrete and Continuous Dynamical Systems - S, 2021, 14 (5) : 1779-1799. doi: 10.3934/dcdss.2020454
[18]

Weiwei Ao, Chao Liu. Asymptotic behavior of sign-changing radial solutions of a semilinear elliptic equation in $ \mathbb{R}^2 $ when exponent approaches $ +\infty $. Discrete and Continuous Dynamical Systems, 2020, 40 (8) : 5047-5077. doi: 10.3934/dcds.2020211
[19]

Ida De Bonis, Daniela Giachetti. Singular parabolic problems with possibly changing sign data. Discrete and Continuous Dynamical Systems - B, 2014, 19 (7) : 2047-2064. doi: 10.3934/dcdsb.2014.19.2047
[20]

J. Húska, Peter Poláčik, M.V. Safonov. Principal eigenvalues, spectral gaps and exponential separation between positive and sign-changing solutions of parabolic equations. Conference Publications, 2005, 2005 (Special) : 427-435. doi: 10.3934/proc.2005.2005.427

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (68)
  • HTML views (0)
  • Cited by (4)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy