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A nonlocal eigenvalue problem for the stability of a traveling wave in a neuronal medium
Evans function and blow-up methods in critical eigenvalue problems
1. | Department of Mathematics, The Ohio State University, Columbus, OH 43210 |
2. | Department of Mathematics, University of Minnesota, Minneapolis, MN 55455, United States |
[1] |
Todd Kapitula, Björn Sandstede. Eigenvalues and resonances using the Evans function. Discrete and Continuous Dynamical Systems, 2004, 10 (4) : 857-869. doi: 10.3934/dcds.2004.10.857 |
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Yuri Latushkin, Alim Sukhtayev. The Evans function and the Weyl-Titchmarsh function. Discrete and Continuous Dynamical Systems - S, 2012, 5 (5) : 939-970. doi: 10.3934/dcdss.2012.5.939 |
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Peter Howard, K. Zumbrun. The Evans function and stability criteria for degenerate viscous shock waves. Discrete and Continuous Dynamical Systems, 2004, 10 (4) : 837-855. doi: 10.3934/dcds.2004.10.837 |
[4] |
Ramon Plaza, K. Zumbrun. An Evans function approach to spectral stability of small-amplitude shock profiles. Discrete and Continuous Dynamical Systems, 2004, 10 (4) : 885-924. doi: 10.3934/dcds.2004.10.885 |
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Jan Burczak, P. Kaplický. Evolutionary, symmetric $p$-Laplacian. Interior regularity of time derivatives and its consequences. Communications on Pure and Applied Analysis, 2016, 15 (6) : 2401-2445. doi: 10.3934/cpaa.2016042 |
[6] |
Martin D. Buhmann, Slawomir Dinew. Limits of radial basis function interpolants. Communications on Pure and Applied Analysis, 2007, 6 (3) : 569-585. doi: 10.3934/cpaa.2007.6.569 |
[7] |
Peter Giesl. Construction of a global Lyapunov function using radial basis functions with a single operator. Discrete and Continuous Dynamical Systems - B, 2007, 7 (1) : 101-124. doi: 10.3934/dcdsb.2007.7.101 |
[8] |
Tomás Sanz-Perela. Regularity of radial stable solutions to semilinear elliptic equations for the fractional Laplacian. Communications on Pure and Applied Analysis, 2018, 17 (6) : 2547-2575. doi: 10.3934/cpaa.2018121 |
[9] |
Elisa Calzolari, Roberta Filippucci, Patrizia Pucci. Existence of radial solutions for the $p$-Laplacian elliptic equations with weights. Discrete and Continuous Dynamical Systems, 2006, 15 (2) : 447-479. doi: 10.3934/dcds.2006.15.447 |
[10] |
Rossella Bartolo, Anna Maria Candela, Addolorata Salvatore. Infinitely many radial solutions of a non--homogeneous $p$--Laplacian problem. Conference Publications, 2013, 2013 (special) : 51-59. doi: 10.3934/proc.2013.2013.51 |
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Xi Wang, Zuhan Liu, Ling Zhou. Asymptotic decay for the classical solution of the chemotaxis system with fractional Laplacian in high dimensions. Discrete and Continuous Dynamical Systems - B, 2018, 23 (9) : 4003-4020. doi: 10.3934/dcdsb.2018121 |
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Mohammad A. Rammaha, Daniel Toundykov, Zahava Wilstein. Global existence and decay of energy for a nonlinear wave equation with $p$-Laplacian damping. Discrete and Continuous Dynamical Systems, 2012, 32 (12) : 4361-4390. doi: 10.3934/dcds.2012.32.4361 |
[13] |
Yaping Wu, Xiuxia Xing, Qixiao Ye. Stability of travelling waves with algebraic decay for $n$-degree Fisher-type equations. Discrete and Continuous Dynamical Systems, 2006, 16 (1) : 47-66. doi: 10.3934/dcds.2006.16.47 |
[14] |
Lihua Min, Xiaoping Yang. Finite speed of propagation and algebraic time decay of solutions to a generalized thin film equation. Communications on Pure and Applied Analysis, 2014, 13 (2) : 543-566. doi: 10.3934/cpaa.2014.13.543 |
[15] |
Trad Alotaibi, D. D. Hai, R. Shivaji. Existence and nonexistence of positive radial solutions for a class of $p$-Laplacian superlinear problems with nonlinear boundary conditions. Communications on Pure and Applied Analysis, 2020, 19 (9) : 4655-4666. doi: 10.3934/cpaa.2020131 |
[16] |
Alfonso Castro, Jorge Cossio, Sigifredo Herrón, Carlos Vélez. Infinitely many radial solutions for a $ p $-Laplacian problem with indefinite weight. Discrete and Continuous Dynamical Systems, 2021, 41 (10) : 4805-4821. doi: 10.3934/dcds.2021058 |
[17] |
Lihong Zhang, Wenwen Hou, Bashir Ahmad, Guotao Wang. Radial symmetry for logarithmic Choquard equation involving a generalized tempered fractional $ p $-Laplacian. Discrete and Continuous Dynamical Systems - S, 2021, 14 (10) : 3851-3863. doi: 10.3934/dcdss.2020445 |
[18] |
Raúl Ferreira, Julio D. Rossi. Decay estimates for a nonlocal $p-$Laplacian evolution problem with mixed boundary conditions. Discrete and Continuous Dynamical Systems, 2015, 35 (4) : 1469-1478. doi: 10.3934/dcds.2015.35.1469 |
[19] |
Ruy Coimbra Charão, Alessandra Piske, Ryo Ikehata. A dissipative logarithmic-Laplacian type of plate equation: Asymptotic profile and decay rates. Discrete and Continuous Dynamical Systems, 2022, 42 (5) : 2215-2255. doi: 10.3934/dcds.2021189 |
[20] |
Olga Bernardi, Matteo Dalla Riva. Analytic dependence on parameters for Evans' approximated Weak KAM solutions. Discrete and Continuous Dynamical Systems, 2017, 37 (9) : 4625-4636. doi: 10.3934/dcds.2017199 |
2020 Impact Factor: 1.392
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