American Institute of Mathematical Sciences

Advanced
  • Previous Article
    A note on singular limits to hyperbolic systems of conservation laws
  • CPAA Home
  • This Issue
  • Next Article
    Breakdown of $C^1$ solution to the Cauchy problem for quasilinear hyperbolic systems with characteristics with constant multiplicity
March  2003, 2(1): 65-76. doi: 10.3934/cpaa.2003.2.65

Positive solutions for a class of reaction-diffusion systems

A. Dall'Acqua 1,

1. 

Department of Applied Analysis, Delft University of Technology, P.O.box 5031, 2600CD Delft, Netherlands

Received  July 2002 Revised  November 2002 Published  December 2002

In this paper we will derive existence of positive solutions for a system of two coupled superlinear elliptic equations with Dirichlet boundary condition. We will use a topological method; in fact the class of systems that we will study does not allow a variational approach. After establishing an a priori estimate for the solutions, we will obtain existence by a continuation method.
Keywords: continuation method., Hardy-Sobolev inequality, Reaction-diffusion systems, a priori estimates.
Mathematics Subject Classification: 35J60, 35J45, 35B4.
Citation: A. Dall'Acqua. Positive solutions for a class of reaction-diffusion systems. Communications on Pure & Applied Analysis, 2003, 2 (1) : 65-76. doi: 10.3934/cpaa.2003.2.65
[1]

José Francisco de Oliveira, João Marcos do Ó, Pedro Ubilla. Hardy-Sobolev type inequality and supercritical extremal problem. Discrete & Continuous Dynamical Systems - A, 2019, 39 (6) : 3345-3364. doi: 10.3934/dcds.2019138
[2]

Jann-Long Chern, Yong-Li Tang, Chuan-Jen Chyan, Yi-Jung Chen. On the uniqueness of singular solutions for a Hardy-Sobolev equation. Conference Publications, 2013, 2013 (special) : 123-128. doi: 10.3934/proc.2013.2013.123
[3]

Svetlana Matculevich, Pekka Neittaanmäki, Sergey Repin. A posteriori error estimates for time-dependent reaction-diffusion problems based on the Payne--Weinberger inequality. Discrete & Continuous Dynamical Systems - A, 2015, 35 (6) : 2659-2677. doi: 10.3934/dcds.2015.35.2659
[4]

Wei Dai, Zhao Liu, Guozhen Lu. Hardy-Sobolev type integral systems with Dirichlet boundary conditions in a half space. Communications on Pure & Applied Analysis, 2017, 16 (4) : 1253-1264. doi: 10.3934/cpaa.2017061
[5]

Mihaela Negreanu, J. Ignacio Tello. On a comparison method to reaction-diffusion systems and its applications to chemotaxis. Discrete & Continuous Dynamical Systems - B, 2013, 18 (10) : 2669-2688. doi: 10.3934/dcdsb.2013.18.2669
[6]

Masato Hashizume, Chun-Hsiung Hsia, Gyeongha Hwang. On the Neumann problem of Hardy-Sobolev critical equations with the multiple singularities. Communications on Pure & Applied Analysis, 2019, 18 (1) : 301-322. doi: 10.3934/cpaa.2019016
[7]

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
[8]

Jinhui Chen, Haitao Yang. A result on Hardy-Sobolev critical elliptic equations with boundary singularities. Communications on Pure & Applied Analysis, 2007, 6 (1) : 191-201. doi: 10.3934/cpaa.2007.6.191
[9]

Klemens Fellner, Wolfang Prager, Bao Q. Tang. The entropy method for reaction-diffusion systems without detailed balance: First order chemical reaction networks. Kinetic & Related Models, 2017, 10 (4) : 1055-1087. doi: 10.3934/krm.2017042
[10]

Ze Cheng, Congming Li. An extended discrete Hardy-Littlewood-Sobolev inequality. Discrete & Continuous Dynamical Systems - A, 2014, 34 (5) : 1951-1959. doi: 10.3934/dcds.2014.34.1951
[11]

Ching-Shan Chou, Yong-Tao Zhang, Rui Zhao, Qing Nie. Numerical methods for stiff reaction-diffusion systems. Discrete & Continuous Dynamical Systems - B, 2007, 7 (3) : 515-525. doi: 10.3934/dcdsb.2007.7.515
[12]

Laurent Desvillettes, Klemens Fellner. Entropy methods for reaction-diffusion systems. Conference Publications, 2007, 2007 (Special) : 304-312. doi: 10.3934/proc.2007.2007.304
[13]

Hongwei Chen. Blow-up estimates of positive solutions of a reaction-diffusion system. Conference Publications, 2003, 2003 (Special) : 182-188. doi: 10.3934/proc.2003.2003.182
[14]

Dieter Bothe, Michel Pierre. The instantaneous limit for reaction-diffusion systems with a fast irreversible reaction. Discrete & Continuous Dynamical Systems - S, 2012, 5 (1) : 49-59. doi: 10.3934/dcdss.2012.5.49
[15]

Guoqing Zhang, Jia-yu Shao, Sanyang Liu. Linking solutions for N-laplace elliptic equations with Hardy-Sobolev operator and indefinite weights. Communications on Pure & Applied Analysis, 2011, 10 (2) : 571-581. doi: 10.3934/cpaa.2011.10.571
[16]

Xin Li, Xingfu Zou. On a reaction-diffusion model for sterile insect release method with release on the boundary. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2509-2522. doi: 10.3934/dcdsb.2012.17.2509
[17]

Patrick De Kepper, István Szalai. An effective design method to produce stationary chemical reaction-diffusion patterns. Communications on Pure & Applied Analysis, 2012, 11 (1) : 189-207. doi: 10.3934/cpaa.2012.11.189
[18]

Genggeng Huang, Congming Li, Ximing Yin. Existence of the maximizing pair for the discrete Hardy-Littlewood-Sobolev inequality. Discrete & Continuous Dynamical Systems - A, 2015, 35 (3) : 935-942. doi: 10.3934/dcds.2015.35.935
[19]

Wei-Jian Bo, Guo Lin, Shigui Ruan. Traveling wave solutions for time periodic reaction-diffusion systems. Discrete & Continuous Dynamical Systems - A, 2018, 38 (9) : 4329-4351. doi: 10.3934/dcds.2018189
[20]

C. van der Mee, Stella Vernier Piro. Travelling waves for solid-gas reaction-diffusion systems. Conference Publications, 2003, 2003 (Special) : 872-879. doi: 10.3934/proc.2003.2003.872

2017 Impact Factor: 0.884

Tools

Metrics

  • PDF downloads (4)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences