American Institute of Mathematical Sciences

Advanced
August  2010, 27(3): 1123-1132. doi: 10.3934/dcds.2010.27.1123

Classes of singular $pq-$Laplacian semipositone systems

Eun Kyoung Lee 1, , R. Shivaji 1, and  Jinglong Ye 1,

1. 

Department of Mathematics and Statistics, Center for Computational Sciences, Mississippi State University, Mississippi State, MS 39762, United States, United States

Received  September 2009 Revised  December 2009 Published  March 2010

We consider the positive solutions to classes of $pq-$Laplacian semipositone systems with Dirichlet boundary conditions, in particular, we study strongly coupled reaction terms which tend to $-\infty$ at the origin and satisfy a combined sublinear condition at $\infty.$ By using the method of sub-super solutions we establish our results.
Keywords: singular semipositone system, sub-super solutions, positive solutions..
Mathematics Subject Classification: Primary: 35J25; Secondary: 35J5.
Citation: Eun Kyoung Lee, R. Shivaji, Jinglong Ye. Classes of singular $pq-$Laplacian semipositone systems. Discrete and Continuous Dynamical Systems, 2010, 27 (3) : 1123-1132. doi: 10.3934/dcds.2010.27.1123
[1]

Yanqin Fang, De Tang. Method of sub-super solutions for fractional elliptic equations. Discrete and Continuous Dynamical Systems - B, 2018, 23 (8) : 3153-3165. doi: 10.3934/dcdsb.2017212
[2]

Maya Chhetri, D. D. Hai, R. Shivaji. On positive solutions for classes of p-Laplacian semipositone systems. Discrete and Continuous Dynamical Systems, 2003, 9 (4) : 1063-1071. doi: 10.3934/dcds.2003.9.1063
[3]

Eun Kyoung Lee, R. Shivaji, Inbo Sim, Byungjae Son. Analysis of positive solutions for a class of semipositone p-Laplacian problems with nonlinear boundary conditions. Communications on Pure and Applied Analysis, 2019, 18 (3) : 1139-1154. doi: 10.3934/cpaa.2019055
[4]

Rui Peng, Xianfa Song, Lei Wei. Existence, nonexistence and uniqueness of positive stationary solutions of a singular Gierer-Meinhardt system. Discrete and Continuous Dynamical Systems, 2017, 37 (8) : 4489-4505. doi: 10.3934/dcds.2017192
[5]

Hiroshi Morishita, Eiji Yanagida, Shoji Yotsutani. Structure of positive radial solutions including singular solutions to Matukuma's equation. Communications on Pure and Applied Analysis, 2005, 4 (4) : 871-888. doi: 10.3934/cpaa.2005.4.871
[6]

Junping Shi, Ratnasingham Shivaji. Exact multiplicity of solutions for classes of semipositone problems with concave-convex nonlinearity. Discrete and Continuous Dynamical Systems, 2001, 7 (3) : 559-571. doi: 10.3934/dcds.2001.7.559
[7]

Yuxia Guo, Jianjun Nie. Classification for positive solutions of degenerate elliptic system. Discrete and Continuous Dynamical Systems, 2019, 39 (3) : 1457-1475. doi: 10.3934/dcds.2018130
[8]

Zaizheng Li, Zhitao Zhang. Uniqueness and nondegeneracy of positive solutions to an elliptic system in ecology. Electronic Research Archive, 2021, 29 (6) : 3761-3774. doi: 10.3934/era.2021060
[9]

Ran Zhuo, Yan Li. Regularity and existence of positive solutions for a fractional system. Communications on Pure and Applied Analysis, 2022, 21 (1) : 83-100. doi: 10.3934/cpaa.2021168
[10]

Rui-Qi Liu, Chun-Lei Tang, Jia-Feng Liao, Xing-Ping Wu. Positive solutions of Kirchhoff type problem with singular and critical nonlinearities in dimension four. Communications on Pure and Applied Analysis, 2016, 15 (5) : 1841-1856. doi: 10.3934/cpaa.2016006
[11]

Zongming Guo, Xuefei Bai. On the global branch of positive radial solutions of an elliptic problem with singular nonlinearity. Communications on Pure and Applied Analysis, 2008, 7 (5) : 1091-1107. doi: 10.3934/cpaa.2008.7.1091
[12]

M. Gaudenzi, P. Habets, F. Zanolin. Positive solutions of superlinear boundary value problems with singular indefinite weight. Communications on Pure and Applied Analysis, 2003, 2 (3) : 411-423. doi: 10.3934/cpaa.2003.2.411
[13]

Xiaomei Sun, Wenyi Chen. Positive solutions for singular elliptic equations with critical Hardy-Sobolev exponent. Communications on Pure and Applied Analysis, 2011, 10 (2) : 527-540. doi: 10.3934/cpaa.2011.10.527
[14]

Tokushi Sato, Tatsuya Watanabe. Singular positive solutions for a fourth order elliptic problem in $R$. Communications on Pure and Applied Analysis, 2011, 10 (1) : 245-268. doi: 10.3934/cpaa.2011.10.245
[15]

Luiz F. O. Faria. Existence and uniqueness of positive solutions for singular biharmonic elliptic systems. Conference Publications, 2015, 2015 (special) : 400-408. doi: 10.3934/proc.2015.0400
[16]

Meiqiang Feng, Yichen Zhang. Positive solutions of singular multiparameter p-Laplacian elliptic systems. Discrete and Continuous Dynamical Systems - B, 2022, 27 (2) : 1121-1147. doi: 10.3934/dcdsb.2021083
[17]

Craig Cowan, Abdolrahman Razani. Singular solutions of a Lane-Emden system. Discrete and Continuous Dynamical Systems, 2021, 41 (2) : 621-656. doi: 10.3934/dcds.2020291
[18]

Linlin Dou. Singular solutions of Toda system in high dimensions. Discrete and Continuous Dynamical Systems, 2022, 42 (7) : 3119-3142. doi: 10.3934/dcds.2022011
[19]

Shu-Yu Hsu. Super fast vanishing solutions of the fast diffusion equation. Discrete and Continuous Dynamical Systems, 2020, 40 (9) : 5383-5414. doi: 10.3934/dcds.2020232
[20]

Yayun Li, Yutian Lei. On existence and nonexistence of positive solutions of an elliptic system with coupled terms. Communications on Pure and Applied Analysis, 2018, 17 (5) : 1749-1764. doi: 10.3934/cpaa.2018083

2021 Impact Factor: 1.588

Tools

Metrics

  • PDF downloads (92)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy