American Institute of Mathematical Sciences

Advanced
2011, 2011(Special): 698-706. doi: 10.3934/proc.2011.2011.698

On critical exponent for an elliptic equation with non-Lipschitz nonlinearity

Yavdat Il'yasov 1,

1. 

Laboratoire de Mathématiques et Applications, Université de La Rochelle, 17042 La Rochelle

Received  July 2010 Revised  March 2011 Published  October 2011

This note deals with weak compact support solutions of an elliptic equation with autonomous non-Lipschitz nonlinearity. Using Pohozaev's identity and the spectral analysis with respect to the ber procedure a critical exponent corresponding to the problem is introduced.
Keywords: Pohozaev's identity, Compact support solution, ber analysis.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
Citation: Yavdat Il'yasov. On critical exponent for an elliptic equation with non-Lipschitz nonlinearity. Conference Publications, 2011, 2011 (Special) : 698-706. doi: 10.3934/proc.2011.2011.698
[1]

Anna Geyer. A note on uniqueness and compact support of solutions in a recent model for tsunami background flows. Communications on Pure and Applied Analysis, 2012, 11 (4) : 1431-1438. doi: 10.3934/cpaa.2012.11.1431
[2]

Salvador Addas-Zanata, Fábio A. Tal. Support of maximizing measures for typical $\mathcal{C}^0$ dynamics on compact manifolds. Discrete and Continuous Dynamical Systems, 2010, 26 (3) : 795-804. doi: 10.3934/dcds.2010.26.795
[3]

Gerhard Rein. Galactic dynamics in MOND---Existence of equilibria with finite mass and compact support. Kinetic and Related Models, 2015, 8 (2) : 381-394. doi: 10.3934/krm.2015.8.381
[4]

Yubo Yuan. Canonical duality solution for alternating support vector machine. Journal of Industrial and Management Optimization, 2012, 8 (3) : 611-621. doi: 10.3934/jimo.2012.8.611
[5]

Pierre Lissy. Construction of gevrey functions with compact support using the bray-mandelbrojt iterative process and applications to the moment method in control theory. Mathematical Control and Related Fields, 2017, 7 (1) : 21-40. doi: 10.3934/mcrf.2017002
[6]

Alireza Ghaffari Hadigheh, Tamás Terlaky. Generalized support set invariancy sensitivity analysis in linear optimization. Journal of Industrial and Management Optimization, 2006, 2 (1) : 1-18. doi: 10.3934/jimo.2006.2.1
[7]

Jian Luo, Shu-Cherng Fang, Yanqin Bai, Zhibin Deng. Fuzzy quadratic surface support vector machine based on fisher discriminant analysis. Journal of Industrial and Management Optimization, 2016, 12 (1) : 357-373. doi: 10.3934/jimo.2016.12.357
[8]

Behrouz Kheirfam, Kamal mirnia. Comments on ''Generalized support set invariancy sensitivity analysis in linear optimization''. Journal of Industrial and Management Optimization, 2008, 4 (3) : 611-616. doi: 10.3934/jimo.2008.4.611
[9]

Saikat Mazumdar. Struwe's decomposition for a polyharmonic operator on a compact Riemannian manifold with or without boundary. Communications on Pure and Applied Analysis, 2017, 16 (1) : 311-330. doi: 10.3934/cpaa.2017015
[10]

Sonja Hohloch, Silvia Sabatini, Daniele Sepe. From compact semi-toric systems to Hamiltonian $S^1$-spaces. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 247-281. doi: 10.3934/dcds.2015.35.247
[11]

Joseph J Kohn. Nirenberg's contributions to complex analysis. Discrete and Continuous Dynamical Systems, 2011, 30 (2) : 537-545. doi: 10.3934/dcds.2011.30.537
[12]

Ye Tian, Wei Yang, Gene Lai, Menghan Zhao. Predicting non-life insurer's insolvency using non-kernel fuzzy quadratic surface support vector machines. Journal of Industrial and Management Optimization, 2019, 15 (2) : 985-999. doi: 10.3934/jimo.2018081
[13]

Andrew Melchionna. The sandpile identity element on an ellipse. Discrete and Continuous Dynamical Systems, 2022  doi: 10.3934/dcds.2022029
[14]

Yu-Hsien Chang, Guo-Chin Jau. The behavior of the solution for a mathematical model for analysis of the cell cycle. Communications on Pure and Applied Analysis, 2006, 5 (4) : 779-792. doi: 10.3934/cpaa.2006.5.779
[15]

J. Leonel Rocha, Sandra M. Aleixo. Dynamical analysis in growth models: Blumberg's equation. Discrete and Continuous Dynamical Systems - B, 2013, 18 (3) : 783-795. doi: 10.3934/dcdsb.2013.18.783
[16]

Jagmohan Tyagi, Ram Baran Verma. Positive solution to extremal Pucci's equations with singular and gradient nonlinearity. Discrete and Continuous Dynamical Systems, 2019, 39 (5) : 2637-2659. doi: 10.3934/dcds.2019110
[17]

Hua Qiu, Shaomei Fang. A BKM's criterion of smooth solution to the incompressible viscoelastic flow. Communications on Pure and Applied Analysis, 2014, 13 (2) : 823-833. doi: 10.3934/cpaa.2014.13.823
[18]

Lei Deng, Jingjie Zhao, Ruimei Wang. Modelling and performance analysis of shuttle-based compact storage systems under different storage policies. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022080
[19]

Xavier Ros-Oton, Joaquim Serra. Local integration by parts and Pohozaev identities for higher order fractional Laplacians. Discrete and Continuous Dynamical Systems, 2015, 35 (5) : 2131-2150. doi: 10.3934/dcds.2015.35.2131
[20]

Alexandre Caboussat, Roland Glowinski. Numerical solution of a variational problem arising in stress analysis: The vector case. Discrete and Continuous Dynamical Systems, 2010, 27 (4) : 1447-1472. doi: 10.3934/dcds.2010.27.1447

 Impact Factor: 

Tools

Metrics

  • PDF downloads (95)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy