American Institute of Mathematical Sciences

Advanced
2007, 2007(Special): 875-882. doi: 10.3934/proc.2007.2007.875

On the influence of the kernel of the bi-harmonic operator on fourth order equations with exponential growth

Frédéric Robert 1,

1. 

Université de Nice-Shopia Antipolis, Laboratorie J.-A. Dieudonné, Parc Valrose, 06108 Nice Cedex 2, France

Received  September 2006 Revised  March 2007 Published  September 2007

Continuing the analysis of [1, 9, 10], we discuss in this note the influence of the Kernel of the bi-harmonic operator $\Delta^2$ on the behavior of families of solutions to $\Delta^2u = e^(4u)$ on a four-dimensional domain of the Euclidean space. We also make a remark on the Paneitz-type equation in the context of compact Riemannian manifolds.
Keywords: Paneitz equation, Exponential growth..
Mathematics Subject Classification: Primary 35J35; Secondary 35B4.
Citation: Frédéric Robert. On the influence of the kernel of the bi-harmonic operator on fourth order equations with exponential growth. Conference Publications, 2007, 2007 (Special) : 875-882. doi: 10.3934/proc.2007.2007.875
[1]

Michael Scheutzow. Exponential growth rate for a singular linear stochastic delay differential equation. Discrete & Continuous Dynamical Systems - B, 2013, 18 (6) : 1683-1696. doi: 10.3934/dcdsb.2013.18.1683
[2]

Federica Sani. A biharmonic equation in $\mathbb{R}^4$ involving nonlinearities with critical exponential growth. Communications on Pure & Applied Analysis, 2013, 12 (1) : 405-428. doi: 10.3934/cpaa.2013.12.405
[3]

Jacek Banasiak, Wilson Lamb. The discrete fragmentation equation: Semigroups, compactness and asynchronous exponential growth. Kinetic & Related Models, 2012, 5 (2) : 223-236. doi: 10.3934/krm.2012.5.223
[4]

Emmanuel Hebey and Frederic Robert. Compactness and global estimates for the geometric Paneitz equation in high dimensions. Electronic Research Announcements, 2004, 10: 135-141.

[5]

John A. D. Appleby, John A. Daniels. Exponential growth in the solution of an affine stochastic differential equation with an average functional and financial market bubbles. Conference Publications, 2011, 2011 (Special) : 91-101. doi: 10.3934/proc.2011.2011.91
[6]

Sami Aouaoui. On some local-nonlocal elliptic equation involving nonlinear terms with exponential growth. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1767-1784. doi: 10.3934/cpaa.2017086
[7]

Sami Aouaoui. On some semilinear equation in $R^4$ containing a Laplacian term and involving nonlinearity with exponential growth. Communications on Pure & Applied Analysis, 2015, 14 (6) : 2185-2201. doi: 10.3934/cpaa.2015.14.2185
[8]

A. Giambruno and M. Zaicev. Minimal varieties of algebras of exponential growth. Electronic Research Announcements, 2000, 6: 40-44.

[9]

Xingwang Xu, Paul C. Yang. Positivity of Paneitz operators. Discrete & Continuous Dynamical Systems - A, 2001, 7 (2) : 329-342. doi: 10.3934/dcds.2001.7.329
[10]

Van Cyr, Bryna Kra. The automorphism group of a minimal shift of stretched exponential growth. Journal of Modern Dynamics, 2016, 10: 483-495. doi: 10.3934/jmd.2016.10.483
[11]

Shuangjie Peng, Jing Zhou. Concentration of solutions for a Paneitz type problem. Discrete & Continuous Dynamical Systems - A, 2010, 26 (3) : 1055-1072. doi: 10.3934/dcds.2010.26.1055
[12]

Kei Matsuura, Mitsuharu Otani. Exponential attractors for a quasilinear parabolic equation. Conference Publications, 2007, 2007 (Special) : 713-720. doi: 10.3934/proc.2007.2007.713
[13]

Nguyen Lam, Guozhen Lu. Existence of nontrivial solutions to Polyharmonic equations with subcritical and critical exponential growth. Discrete & Continuous Dynamical Systems - A, 2012, 32 (6) : 2187-2205. doi: 10.3934/dcds.2012.32.2187
[14]

Christian Bonatti, Lorenzo J. Díaz, Todd Fisher. Super-exponential growth of the number of periodic orbits inside homoclinic classes. Discrete & Continuous Dynamical Systems - A, 2008, 20 (3) : 589-604. doi: 10.3934/dcds.2008.20.589
[15]

Carlos Castillo-Garsow. The role of multiple modeling perspectives in students' learning of exponential growth. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1437-1453. doi: 10.3934/mbe.2013.10.1437
[16]

Jiguang Bao, Nguyen Lam, Guozhen Lu. Polyharmonic equations with critical exponential growth in the whole space $ \mathbb{R}^{n}$. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 577-600. doi: 10.3934/dcds.2016.36.577
[17]

Artur Avila, Thomas Roblin. Uniform exponential growth for some SL(2, R) matrix products. Journal of Modern Dynamics, 2009, 3 (4) : 549-554. doi: 10.3934/jmd.2009.3.549
[18]

Dung Le. Exponential attractors for a chemotaxis growth system on domains of arbitrary dimension. Conference Publications, 2003, 2003 (Special) : 536-543. doi: 10.3934/proc.2003.2003.536
[19]

João Marcos do Ó, Bruno Ribeiro, Bernhard Ruf. Hamiltonian elliptic systems in dimension two with arbitrary and double exponential growth conditions. Discrete & Continuous Dynamical Systems - A, 2019, 0 (0) : 0-0. doi: 10.3934/dcds.2020138
[20]

Horst R. Thieme. Positive perturbation of operator semigroups: growth bounds, essential compactness and asynchronous exponential growth. Discrete & Continuous Dynamical Systems - A, 1998, 4 (4) : 735-764. doi: 10.3934/dcds.1998.4.735

 Impact Factor: 

Tools

Metrics

  • PDF downloads (10)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences