2005, 2005(Special): 510-517. doi: 10.3934/proc.2005.2005.510

On lane-emden type systems

1. 

Department Of Mathematical Sciences, University Of Cincinnati, Cincinnati Ohio 45221-0025

2. 

Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187, United States

Received  September 2004 Revised  April 2005 Published  September 2005

We consider a class of singular systems of Lane-Emden type \begin{equation} \nonumber \begin{cases} \Delta u + \la u^{p_1} v^{q_1}=0, & x\in D,\\ \Delta v + \la u^{p_2} v^{q_2}=0, & x\in D,\\ u=v=0, & x\in \partial D, \end{cases} \end{equation} with $p_1\le 0, \; p_2> 0, \; q_1> 0, \; q_2\le 0$, and $D$ a smooth domain in $\R^n$. In case the system is sublinear we prove existence of a positive solution. If $D$ is a ball in $\R^n$, we prove both existence and uniqueness of positive radially symmetric solution.
Citation: Philip Korman, Junping Shi. On lane-emden type systems. Conference Publications, 2005, 2005 (Special) : 510-517. doi: 10.3934/proc.2005.2005.510
[1]

Rafael Ortega, James R. Ward Jr. A semilinear elliptic system with vanishing nonlinearities. Conference Publications, 2003, 2003 (Special) : 688-693. doi: 10.3934/proc.2003.2003.688

[2]

Ruofei Yao, Yi Li, Hongbin Chen. Uniqueness of positive radial solutions of a semilinear elliptic equation in an annulus. Discrete & Continuous Dynamical Systems - A, 2018, 0 (0) : 1-10. doi: 10.3934/dcds.2018122

[3]

Diane Denny. A unique positive solution to a system of semilinear elliptic equations. Conference Publications, 2013, 2013 (special) : 193-195. doi: 10.3934/proc.2013.2013.193

[4]

Dongho Chae. Existence of a semilinear elliptic system with exponential nonlinearities. Discrete & Continuous Dynamical Systems - A, 2007, 18 (4) : 709-718. doi: 10.3934/dcds.2007.18.709

[5]

Shiren Zhu, Xiaoli Chen, Jianfu Yang. Regularity, symmetry and uniqueness of positive solutions to a nonlinear elliptic system. Communications on Pure & Applied Analysis, 2013, 12 (6) : 2685-2696. doi: 10.3934/cpaa.2013.12.2685

[6]

Philip Korman. On uniqueness of positive solutions for a class of semilinear equations. Discrete & Continuous Dynamical Systems - A, 2002, 8 (4) : 865-871. doi: 10.3934/dcds.2002.8.865

[7]

Lei Wei, Zhaosheng Feng. Isolated singularity for semilinear elliptic equations. Discrete & Continuous Dynamical Systems - A, 2015, 35 (7) : 3239-3252. doi: 10.3934/dcds.2015.35.3239

[8]

Hwai-Chiuan Wang. On domains and their indexes with applications to semilinear elliptic equations. Discrete & Continuous Dynamical Systems - A, 2007, 19 (2) : 447-467. doi: 10.3934/dcds.2007.19.447

[9]

Claudia Anedda, Giovanni Porru. Boundary estimates for solutions of weighted semilinear elliptic equations. Discrete & Continuous Dynamical Systems - A, 2012, 32 (11) : 3801-3817. doi: 10.3934/dcds.2012.32.3801

[10]

V. Lakshmikantham, S. Leela. Generalized quasilinearization and semilinear degenerate elliptic problems. Discrete & Continuous Dynamical Systems - A, 2001, 7 (4) : 801-808. doi: 10.3934/dcds.2001.7.801

[11]

Henri Berestycki, Juncheng Wei. On least energy solutions to a semilinear elliptic equation in a strip. Discrete & Continuous Dynamical Systems - A, 2010, 28 (3) : 1083-1099. doi: 10.3934/dcds.2010.28.1083

[12]

Antonio Greco, Marcello Lucia. Gamma-star-shapedness for semilinear elliptic equations. Communications on Pure & Applied Analysis, 2005, 4 (1) : 93-99. doi: 10.3934/cpaa.2005.4.93

[13]

Marco Degiovanni, Michele Scaglia. A variational approach to semilinear elliptic equations with measure data. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1233-1248. doi: 10.3934/dcds.2011.31.1233

[14]

Jiabao Su, Zhaoli Liu. A bounded resonance problem for semilinear elliptic equations. Discrete & Continuous Dynamical Systems - A, 2007, 19 (2) : 431-445. doi: 10.3934/dcds.2007.19.431

[15]

Hwai-Chiuan Wang. Stability and symmetry breaking of solutions of semilinear elliptic equations. Conference Publications, 2005, 2005 (Special) : 886-894. doi: 10.3934/proc.2005.2005.886

[16]

David L. Finn. Convexity of level curves for solutions to semilinear elliptic equations. Communications on Pure & Applied Analysis, 2008, 7 (6) : 1335-1343. doi: 10.3934/cpaa.2008.7.1335

[17]

Junping Shi, R. Shivaji. Semilinear elliptic equations with generalized cubic nonlinearities. Conference Publications, 2005, 2005 (Special) : 798-805. doi: 10.3934/proc.2005.2005.798

[18]

Xavier Cabré, Manel Sanchón, Joel Spruck. A priori estimates for semistable solutions of semilinear elliptic equations. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 601-609. doi: 10.3934/dcds.2016.36.601

[19]

Mousomi Bhakta, Debangana Mukherjee. Semilinear nonlocal elliptic equations with critical and supercritical exponents. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1741-1766. doi: 10.3934/cpaa.2017085

[20]

C. Cortázar, Marta García-Huidobro. On the uniqueness of ground state solutions of a semilinear equation containing a weighted Laplacian. Communications on Pure & Applied Analysis, 2006, 5 (4) : 813-826. doi: 10.3934/cpaa.2006.5.813

 Impact Factor: 

Metrics

  • PDF downloads (3)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]