October  2001, 7(4): 801-808. doi: 10.3934/dcds.2001.7.801

Generalized quasilinearization and semilinear degenerate elliptic problems

1. 

Department of Mathematics, Florida Institute of Technology, Melbourne, FL 32901

2. 

Department of Mathematics, SUNY at Geneseo, Geneseo, NY 14454, United States

Received  October 2000 Published  July 2001

The method of generalized quasilinearization is extended to semilinear degenerate elliptic boundary value problems.
Citation: 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
[1]

T. Gnana Bhaskar, S. Köksal, V. Lakshmikantham. Generalized quasilinearization method for semilinear hyperbolic problems. Discrete & Continuous Dynamical Systems - A, 2003, 9 (5) : 1263-1275. doi: 10.3934/dcds.2003.9.1263

[2]

Agnese Di Castro, Mayte Pérez-Llanos, José Miguel Urbano. Limits of anisotropic and degenerate elliptic problems. Communications on Pure & Applied Analysis, 2012, 11 (3) : 1217-1229. doi: 10.3934/cpaa.2012.11.1217

[3]

Charles A. Stuart. Stability analysis for a family of degenerate semilinear parabolic problems. Discrete & Continuous Dynamical Systems - A, 2018, 38 (10) : 5297-5337. doi: 10.3934/dcds.2018234

[4]

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

[5]

Rong Xiao, Yuying Zhou. Multiple solutions for a class of semilinear elliptic variational inclusion problems. Journal of Industrial & Management Optimization, 2011, 7 (4) : 991-1002. doi: 10.3934/jimo.2011.7.991

[6]

Shujie Li, Zhitao Zhang. Multiple solutions theorems for semilinear elliptic boundary value problems with resonance at infinity. Discrete & Continuous Dynamical Systems - A, 1999, 5 (3) : 489-493. doi: 10.3934/dcds.1999.5.489

[7]

Zongming Guo, Yunting Yu. Boundary value problems for a semilinear elliptic equation with singular nonlinearity. Communications on Pure & Applied Analysis, 2016, 15 (2) : 399-412. doi: 10.3934/cpaa.2016.15.399

[8]

Shun Kodama. A concentration phenomenon of the least energy solution to non-autonomous elliptic problems with a totally degenerate potential. Communications on Pure & Applied Analysis, 2017, 16 (2) : 671-698. doi: 10.3934/cpaa.2017033

[9]

Florin Catrina, Zhi-Qiang Wang. Asymptotic uniqueness and exact symmetry of k-bump solutions for a class of degenerate elliptic problems. Conference Publications, 2001, 2001 (Special) : 80-87. doi: 10.3934/proc.2001.2001.80

[10]

Asadollah Aghajani. Regularity of extremal solutions of semilinear elliptic problems with non-convex nonlinearities on general domains. Discrete & Continuous Dynamical Systems - A, 2017, 37 (7) : 3521-3530. doi: 10.3934/dcds.2017150

[11]

Gabriele Cora, Alessandro Iacopetti. Sign-changing bubble-tower solutions to fractional semilinear elliptic problems. Discrete & Continuous Dynamical Systems - A, 2019, 39 (10) : 6149-6173. doi: 10.3934/dcds.2019268

[12]

Brooke L. Hollingsworth, R.E. Showalter. Semilinear degenerate parabolic systems and distributed capacitance models. Discrete & Continuous Dynamical Systems - A, 1995, 1 (1) : 59-76. doi: 10.3934/dcds.1995.1.59

[13]

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

[14]

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

[15]

Teemu Lukkari, Mikko Parviainen. Stability of degenerate parabolic Cauchy problems. Communications on Pure & Applied Analysis, 2015, 14 (1) : 201-216. doi: 10.3934/cpaa.2015.14.201

[16]

Florian De Vuyst, Francesco Salvarani. Numerical simulations of degenerate transport problems. Kinetic & Related Models, 2014, 7 (3) : 463-476. doi: 10.3934/krm.2014.7.463

[17]

Annamaria Canino, Elisa De Giorgio, Berardino Sciunzi. Second order regularity for degenerate nonlinear elliptic equations. Discrete & Continuous Dynamical Systems - A, 2018, 38 (8) : 4231-4242. doi: 10.3934/dcds.2018184

[18]

Genggeng Huang. A Liouville theorem of degenerate elliptic equation and its application. Discrete & Continuous Dynamical Systems - A, 2013, 33 (10) : 4549-4566. doi: 10.3934/dcds.2013.33.4549

[19]

Giuseppe Di Fazio, Maria Stella Fanciullo, Pietro Zamboni. Harnack inequality for degenerate elliptic equations and sum operators. Communications on Pure & Applied Analysis, 2015, 14 (6) : 2363-2376. doi: 10.3934/cpaa.2015.14.2363

[20]

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

2018 Impact Factor: 1.143

Metrics

  • PDF downloads (7)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]