American Institute of Mathematical Sciences

Advanced
  • Previous Article
    On the higher-order global regularity of the inviscid Voigt-regularization of three-dimensional hydrodynamic models
  • DCDS-B Home
  • This Issue
  • Next Article
    Remarks on a paper of Kotani concerning generalized reflectionless Schrödinger potentials
September  2010, 14(2): 587-602. doi: 10.3934/dcdsb.2010.14.587

Polynomial reformulation of the Kuo criteria for v- sufficiency of map-germs

Victor Kozyakin 1,

1. 

Institute for Information Transmission Problems, Russian Academy of Sciences, Bolshoj Karetny lane 19, Moscow 127994 GSP-4

Received  July 2009 Published  June 2010

In the paper a set of necessary and sufficient conditions for v-sufficiency (equiv. sv-sufficiency) of jets of map-germs $f:(\mathbb{R}^{n},0)\to (\mathbb{R}^{m},0)$ is proved which generalize both the Kuiper-Kuo and the Thom conditions in the function case ($m=1$) so as the Kuo conditions in the general map case ($m>1$). Contrary to the Kuo conditions the conditions proved in the paper do not require to verify any inequalities in a so-called horn-neighborhood of the (a'priori unknown) set $f^{-1}(0)$. Instead, the proposed conditions reduce the problem on v-sufficiency of jets to evaluating the local Łojasiewicz exponents for some constructively built polynomial functions.
Keywords: Łojasiewicz exponent, sufficiency of map-germs, critical points., Finite determinedness, truncated equations.
Mathematics Subject Classification: Primary: 58K40; 58K45; Secondary: 32S1.
Citation: Victor Kozyakin. Polynomial reformulation of the Kuo criteria for v- sufficiency of map-germs. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 587-602. doi: 10.3934/dcdsb.2010.14.587
[1]

Boris Paneah. On the over determinedness of some functional equations. Discrete & Continuous Dynamical Systems, 2004, 10 (1&2) : 497-505. doi: 10.3934/dcds.2004.10.497
[2]

Massimo Grossi. On the number of critical points of solutions of semilinear elliptic equations. Electronic Research Archive, , () : -. doi: 10.3934/era.2021080
[3]

Fengjuan Meng, Chengkui Zhong. Multiple equilibrium points in global attractor for the weakly damped wave equation with critical exponent. Discrete & Continuous Dynamical Systems - B, 2014, 19 (1) : 217-230. doi: 10.3934/dcdsb.2014.19.217
[4]

Li Ma. Blow-up for semilinear parabolic equations with critical Sobolev exponent. Communications on Pure & Applied Analysis, 2013, 12 (2) : 1103-1110. doi: 10.3934/cpaa.2013.12.1103
[5]

Xiaomei Sun, Wenyi Chen. Positive solutions for singular elliptic equations with critical Hardy-Sobolev exponent. Communications on Pure & Applied Analysis, 2011, 10 (2) : 527-540. doi: 10.3934/cpaa.2011.10.527
[6]

Peng Chen, Xiaochun Liu. Multiplicity of solutions to Kirchhoff type equations with critical Sobolev exponent. Communications on Pure & Applied Analysis, 2018, 17 (1) : 113-125. doi: 10.3934/cpaa.2018007
[7]

Kaimin Teng, Xiumei He. Ground state solutions for fractional Schrödinger equations with critical Sobolev exponent. Communications on Pure & Applied Analysis, 2016, 15 (3) : 991-1008. doi: 10.3934/cpaa.2016.15.991
[8]

Shengfan Zhou, Linshan Wang. Kernel sections for damped non-autonomous wave equations with critical exponent. Discrete & Continuous Dynamical Systems, 2003, 9 (2) : 399-412. doi: 10.3934/dcds.2003.9.399
[9]

Yu Chen, Yanheng Ding, Suhong Li. Existence and concentration for Kirchhoff type equations around topologically critical points of the potential. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1641-1671. doi: 10.3934/cpaa.2017079
[10]

Enrique R. Pujals, Federico Rodriguez Hertz. Critical points for surface diffeomorphisms. Journal of Modern Dynamics, 2007, 1 (4) : 615-648. doi: 10.3934/jmd.2007.1.615
[11]

Keith Promislow, Hang Zhang. Critical points of functionalized Lagrangians. Discrete & Continuous Dynamical Systems, 2013, 33 (4) : 1231-1246. doi: 10.3934/dcds.2013.33.1231
[12]

Qingfang Wang, Hua Yang. Solutions of nonlocal problem with critical exponent. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5591-5608. doi: 10.3934/cpaa.2020253
[13]

Yanfang Peng. On elliptic systems with Sobolev critical exponent. Discrete & Continuous Dynamical Systems, 2016, 36 (6) : 3357-3373. doi: 10.3934/dcds.2016.36.3357
[14]

Matthieu Alfaro, Isabeau Birindelli. Evolution equations involving nonlinear truncated Laplacian operators. Discrete & Continuous Dynamical Systems, 2020, 40 (6) : 3057-3073. doi: 10.3934/dcds.2020046
[15]

Fengshuang Gao, Yuxia Guo. Infinitely many solutions for quasilinear equations with critical exponent and Hardy potential in $ \mathbb{R}^N $. Discrete & Continuous Dynamical Systems, 2020, 40 (9) : 5591-5616. doi: 10.3934/dcds.2020239
[16]

A. Kh. Khanmamedov. Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent. Discrete & Continuous Dynamical Systems, 2011, 31 (1) : 119-138. doi: 10.3934/dcds.2011.31.119
[17]

Björn Birnir, Kenneth Nelson. The existence of smooth attractors of damped and driven nonlinear wave equations with critical exponent , s = 5. Conference Publications, 1998, 1998 (Special) : 100-117. doi: 10.3934/proc.1998.1998.100
[18]

Wenmin Gong, Guangcun Lu. On Dirac equation with a potential and critical Sobolev exponent. Communications on Pure & Applied Analysis, 2015, 14 (6) : 2231-2263. doi: 10.3934/cpaa.2015.14.2231
[19]

Maurizio Grasselli, Vittorino Pata. On the damped semilinear wave equation with critical exponent. Conference Publications, 2003, 2003 (Special) : 351-358. doi: 10.3934/proc.2003.2003.351
[20]

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 & Applied Analysis, 2013, 12 (6) : 2697-2713. doi: 10.3934/cpaa.2013.12.2697

2020 Impact Factor: 1.327

Tools

Metrics

  • PDF downloads (59)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences