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On the uniqueness of ground state solutions of a semilinear equation containing a weighted Laplacian
Spike solutions to a nonlocal differential equation
1. | Department of Mathematics, University of Connecticut, 196 Auditorium Road, U-3009, Storrs, CT 06269-3009, United States |
2. | Department of Mathematics, Jackson State University, P.O. Box 17610, Jackson, MS 39217, United States |
[1] |
Nabil T. Fadai, Michael J. Ward, Juncheng Wei. A time-delay in the activator kinetics enhances the stability of a spike solution to the gierer-meinhardt model. Discrete and Continuous Dynamical Systems - B, 2018, 23 (4) : 1431-1458. doi: 10.3934/dcdsb.2018158 |
[2] |
Theodore Kolokolnikov, Michael J. Ward. Bifurcation of spike equilibria in the near-shadow Gierer-Meinhardt model. Discrete and Continuous Dynamical Systems - B, 2004, 4 (4) : 1033-1064. doi: 10.3934/dcdsb.2004.4.1033 |
[3] |
Nancy Khalil, David Iron, Theodore Kolokolnikov. Stability and dynamics of spike-type solutions to delayed Gierer-Meinhardt equations. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022117 |
[4] |
Shin-Ichiro Ei, Kota Ikeda, Yasuhito Miyamoto. Dynamics of a boundary spike for the shadow Gierer-Meinhardt system. Communications on Pure and Applied Analysis, 2012, 11 (1) : 115-145. doi: 10.3934/cpaa.2012.11.115 |
[5] |
Siu-Long Lei. Adaptive method for spike solutions of Gierer-Meinhardt system on irregular domain. Discrete and Continuous Dynamical Systems - B, 2011, 15 (3) : 651-668. doi: 10.3934/dcdsb.2011.15.651 |
[6] |
Georgia Karali, Takashi Suzuki, Yoshio Yamada. Global-in-time behavior of the solution to a Gierer-Meinhardt system. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 2885-2900. doi: 10.3934/dcds.2013.33.2885 |
[7] |
Juncheng Wei, Matthias Winter. On the Gierer-Meinhardt system with precursors. Discrete and Continuous Dynamical Systems, 2009, 25 (1) : 363-398. doi: 10.3934/dcds.2009.25.363 |
[8] |
Manuel del Pino, Patricio Felmer, Michal Kowalczyk. Boundary spikes in the Gierer-Meinhardt system. Communications on Pure and Applied Analysis, 2002, 1 (4) : 437-456. doi: 10.3934/cpaa.2002.1.437 |
[9] |
Henghui Zou. On global existence for the Gierer-Meinhardt system. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 583-591. doi: 10.3934/dcds.2015.35.583 |
[10] |
Mengxin Chen, Ranchao Wu, Yancong Xu. Dynamics of a depletion-type Gierer-Meinhardt model with Langmuir-Hinshelwood reaction scheme. Discrete and Continuous Dynamical Systems - B, 2022, 27 (4) : 2275-2312. doi: 10.3934/dcdsb.2021132 |
[11] |
Jan-Phillip Bäcker, Matthias Röger. Analysis and asymptotic reduction of a bulk-surface reaction-diffusion model of Gierer-Meinhardt type. Communications on Pure and Applied Analysis, 2022, 21 (4) : 1139-1155. doi: 10.3934/cpaa.2022013 |
[12] |
Kota Ikeda. The existence and uniqueness of unstable eigenvalues for stripe patterns in the Gierer-Meinhardt system. Networks and Heterogeneous Media, 2013, 8 (1) : 291-325. doi: 10.3934/nhm.2013.8.291 |
[13] |
Rui Peng, Xianfa Song, Lei Wei. Existence, nonexistence and uniqueness of positive stationary solutions of a singular Gierer-Meinhardt system. Discrete and Continuous Dynamical Systems, 2017, 37 (8) : 4489-4505. doi: 10.3934/dcds.2017192 |
[14] |
Kazuhiro Kurata, Kotaro Morimoto. Construction and asymptotic behavior of multi-peak solutions to the Gierer-Meinhardt system with saturation. Communications on Pure and Applied Analysis, 2008, 7 (6) : 1443-1482. doi: 10.3934/cpaa.2008.7.1443 |
[15] |
Chunqing Lu. Existence and uniqueness of single spike solution of the carrier-pearson problem. Conference Publications, 2001, 2001 (Special) : 259-264. doi: 10.3934/proc.2001.2001.259 |
[16] |
Antonio Di Crescenzo, Maria Longobardi, Barbara Martinucci. On a spike train probability model with interacting neural units. Mathematical Biosciences & Engineering, 2014, 11 (2) : 217-231. doi: 10.3934/mbe.2014.11.217 |
[17] |
Mi-Young Kim. Uniqueness and stability of positive periodic numerical solution of an epidemic model. Discrete and Continuous Dynamical Systems - B, 2007, 7 (2) : 365-375. doi: 10.3934/dcdsb.2007.7.365 |
[18] |
Aniello Buonocore, Luigia Caputo, Enrica Pirozzi, Maria Francesca Carfora. A leaky integrate-and-fire model with adaptation for the generation of a spike train. Mathematical Biosciences & Engineering, 2016, 13 (3) : 483-493. doi: 10.3934/mbe.2016002 |
[19] |
Giuseppe D'Onofrio, Enrica Pirozzi. Successive spike times predicted by a stochastic neuronal model with a variable input signal. Mathematical Biosciences & Engineering, 2016, 13 (3) : 495-507. doi: 10.3934/mbe.2016003 |
[20] |
Yajing Zhang, Xinfu Chen, Jianghao Hao, Xin Lai, Cong Qin. Dynamics of spike in a Keller-Segel's minimal chemotaxis model. Discrete and Continuous Dynamical Systems, 2017, 37 (2) : 1109-1127. doi: 10.3934/dcds.2017046 |
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