American Institute of Mathematical Sciences

Advanced
June  2010, 28(2): 809-826. doi: 10.3934/dcds.2010.28.809

On a new index theory and non semi-trivial solutions for elliptic systems

Kung-Ching Chang 1, , Zhi-Qiang Wang 2, and  Tan Zhang 3,

1. 

School of Mathematical Sciences, Peking University, Beijing 100871, China
2. 

Department of Mathematics and Statistics, Utah State University, Logan, UT 84322
3. 

Department of Mathematics and Statistics, Murray State University, Murray, KY 42071, United States

Received  February 2010 Revised  April 2010 Published  April 2010

Two indices, which are similar to the Krasnoselski's genus on thesphere, are defined on the product of spheres. They are applied toinvestigate the multiple non semi-trivial solutions for ellipticsystems. Both constraint and unconstraint problems are studied.
Keywords: genus., Elliptic system, eigenvalue, critical point theory.
Mathematics Subject Classification: 35J50, 58E0.
Citation: Kung-Ching Chang, Zhi-Qiang Wang, Tan Zhang. On a new index theory and non semi-trivial solutions for elliptic systems. Discrete and Continuous Dynamical Systems, 2010, 28 (2) : 809-826. doi: 10.3934/dcds.2010.28.809
[1]

Salvatore A. Marano, Sunra J. N. Mosconi. Multiple solutions to elliptic inclusions via critical point theory on closed convex sets. Discrete and Continuous Dynamical Systems, 2015, 35 (7) : 3087-3102. doi: 10.3934/dcds.2015.35.3087
[2]

Jingxian Sun, Shouchuan Hu. Flow-invariant sets and critical point theory. Discrete and Continuous Dynamical Systems, 2003, 9 (2) : 483-496. doi: 10.3934/dcds.2003.9.483
[3]

Antonio Ambrosetti, Massimiliano Berti. Applications of critical point theory to homoclinics and complex dynamics. Conference Publications, 1998, 1998 (Special) : 72-78. doi: 10.3934/proc.1998.1998.72
[4]

Lucas C. F. Ferreira, Everaldo Medeiros, Marcelo Montenegro. An elliptic system and the critical hyperbola. Communications on Pure and Applied Analysis, 2015, 14 (3) : 1169-1182. doi: 10.3934/cpaa.2015.14.1169
[5]

Salvatore A. Marano, Sunra Mosconi. Non-smooth critical point theory on closed convex sets. Communications on Pure and Applied Analysis, 2014, 13 (3) : 1187-1202. doi: 10.3934/cpaa.2014.13.1187
[6]

Futoshi Takahashi. An eigenvalue problem related to blowing-up solutions for a semilinear elliptic equation with the critical Sobolev exponent. Discrete and Continuous Dynamical Systems - S, 2011, 4 (4) : 907-922. doi: 10.3934/dcdss.2011.4.907
[7]

Mónica Clapp, Jorge Faya. Multiple solutions to a weakly coupled purely critical elliptic system in bounded domains. Discrete and Continuous Dynamical Systems, 2019, 39 (6) : 3265-3289. doi: 10.3934/dcds.2019135
[8]

Olivier Druet, Emmanuel Hebey and Frederic Robert. A $C^0$-theory for the blow-up of second order elliptic equations of critical Sobolev growth. Electronic Research Announcements, 2003, 9: 19-25.

[9]

Philip N. J. Eagle, Steven D. Galbraith, John B. Ong. Point compression for Koblitz elliptic curves. Advances in Mathematics of Communications, 2011, 5 (1) : 1-10. doi: 10.3934/amc.2011.5.1
[10]

Jann-Long Chern, Sze-Guang Yang, Zhi-You Chen, Chih-Her Chen. On the family of non-topological solutions for the elliptic system arising from a product Abelian gauge field theory. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3291-3304. doi: 10.3934/dcds.2020127
[11]

Tomasz Cieślak, Kentarou Fujie. Global existence in the 1D quasilinear parabolic-elliptic chemotaxis system with critical nonlinearity. Discrete and Continuous Dynamical Systems - S, 2020, 13 (2) : 165-176. doi: 10.3934/dcdss.2020009
[12]

Anna Maria Candela, Giuliana Palmieri. Some abstract critical point theorems and applications. Conference Publications, 2009, 2009 (Special) : 133-142. doi: 10.3934/proc.2009.2009.133
[13]

Domingo González, Gamaliel Blé. Core entropy of polynomials with a critical point of maximal order. Discrete and Continuous Dynamical Systems, 2019, 39 (1) : 115-130. doi: 10.3934/dcds.2019005
[14]

Björn Sandstede, Arnd Scheel. Evans function and blow-up methods in critical eigenvalue problems. Discrete and Continuous Dynamical Systems, 2004, 10 (4) : 941-964. doi: 10.3934/dcds.2004.10.941
[15]

Yanfang Peng. On elliptic systems with Sobolev critical exponent. Discrete and Continuous Dynamical Systems, 2016, 36 (6) : 3357-3373. doi: 10.3934/dcds.2016.36.3357
[16]

Lipeng Duan, Shuying Tian. Concentrated solutions for a critical elliptic equation. Discrete and Continuous Dynamical Systems, 2022  doi: 10.3934/dcds.2022046
[17]

Antonio Garcia. Transition tori near an elliptic-fixed point. Discrete and Continuous Dynamical Systems, 2000, 6 (2) : 381-392. doi: 10.3934/dcds.2000.6.381
[18]

Aixia Qian, Shujie Li. Multiple sign-changing solutions of an elliptic eigenvalue problem. Discrete and Continuous Dynamical Systems, 2005, 12 (4) : 737-746. doi: 10.3934/dcds.2005.12.737
[19]

Inbo Sim, Yun-Ho Kim. Existence of solutions and positivity of the infimum eigenvalue for degenerate elliptic equations with variable exponents. Conference Publications, 2013, 2013 (special) : 695-707. doi: 10.3934/proc.2013.2013.695
[20]

Chiu-Yen Kao, Yuan Lou, Eiji Yanagida. Principal eigenvalue for an elliptic problem with indefinite weight on cylindrical domains. Mathematical Biosciences & Engineering, 2008, 5 (2) : 315-335. doi: 10.3934/mbe.2008.5.315

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (94)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy