American Institute of Mathematical Sciences

Advanced
January  2003, 9(1): 55-68. doi: 10.3934/dcds.2003.9.55

Positive solutions to a class of quasilinear elliptic equations on $\mathbb R$

Antonio Ambrosetti 1, and  Zhi-Qiang Wang 2,

1. 

SISSA, via Beirut, 2-4, 34014 Trieste TS, Italy
2. 

Department of Mathematics and Statistics, Utah State University, Logan, UT 84322, USA, United States

Received  August 2002 Revised  November 2003 Published  November 2003

We discuss the existence of positive solutions of perturbation to a class of quasilinear elliptic equations on $\mathbb R$.
Keywords: perturbation theory., Fully nonlinear elliptic equations.
Mathematics Subject Classification: 35Hxx.
Citation: Antonio Ambrosetti, Zhi-Qiang Wang. Positive solutions to a class of quasilinear elliptic equations on $\mathbb R$. Discrete & Continuous Dynamical Systems, 2003, 9 (1) : 55-68. doi: 10.3934/dcds.2003.9.55
[1]

Limei Dai. Entire solutions with asymptotic behavior of fully nonlinear uniformly elliptic equations. Communications on Pure & Applied Analysis, 2011, 10 (6) : 1707-1714. doi: 10.3934/cpaa.2011.10.1707
[2]

Pierpaolo Soravia. Uniqueness results for fully nonlinear degenerate elliptic equations with discontinuous coefficients. Communications on Pure & Applied Analysis, 2006, 5 (1) : 213-240. doi: 10.3934/cpaa.2006.5.213
[3]

Hongxia Zhang, Ying Wang. Liouville results for fully nonlinear integral elliptic equations in exterior domains. Communications on Pure & Applied Analysis, 2018, 17 (1) : 85-112. doi: 10.3934/cpaa.2018006
[4]

Chunhui Qiu, Rirong Yuan. On the Dirichlet problem for fully nonlinear elliptic equations on annuli of metric cones. Discrete & Continuous Dynamical Systems, 2017, 37 (11) : 5707-5730. doi: 10.3934/dcds.2017247
[5]

Lidan Wang, Lihe Wang, Chunqin Zhou. Classification of positive solutions for fully nonlinear elliptic equations in unbounded cylinders. Communications on Pure & Applied Analysis, 2021, 20 (3) : 1241-1261. doi: 10.3934/cpaa.2021019
[6]

Martino Bardi, Paola Mannucci. On the Dirichlet problem for non-totally degenerate fully nonlinear elliptic equations. Communications on Pure & Applied Analysis, 2006, 5 (4) : 709-731. doi: 10.3934/cpaa.2006.5.709
[7]

Antonio Vitolo, Maria E. Amendola, Giulio Galise. On the uniqueness of blow-up solutions of fully nonlinear elliptic equations. Conference Publications, 2013, 2013 (special) : 771-780. doi: 10.3934/proc.2013.2013.771
[8]

Agnid Banerjee. A note on the unique continuation property for fully nonlinear elliptic equations. Communications on Pure & Applied Analysis, 2015, 14 (2) : 623-626. doi: 10.3934/cpaa.2015.14.623
[9]

John Boyd. Strongly nonlinear perturbation theory for solitary waves and bions. Evolution Equations & Control Theory, 2019, 8 (1) : 1-29. doi: 10.3934/eect.2019001
[10]

Paola Mannucci. The Dirichlet problem for fully nonlinear elliptic equations non-degenerate in a fixed direction. Communications on Pure & Applied Analysis, 2014, 13 (1) : 119-133. doi: 10.3934/cpaa.2014.13.119
[11]

Fabio Punzo. Phragmèn-Lindelöf principles for fully nonlinear elliptic equations with unbounded coefficients. Communications on Pure & Applied Analysis, 2010, 9 (5) : 1439-1461. doi: 10.3934/cpaa.2010.9.1439
[12]

Italo Capuzzo Dolcetta, Antonio Vitolo. Glaeser's type gradient estimates for non-negative solutions of fully nonlinear elliptic equations. Discrete & Continuous Dynamical Systems, 2010, 28 (2) : 539-557. doi: 10.3934/dcds.2010.28.539
[13]

Luca Rossi. Non-existence of positive solutions of fully nonlinear elliptic equations in unbounded domains. Communications on Pure & Applied Analysis, 2008, 7 (1) : 125-141. doi: 10.3934/cpaa.2008.7.125
[14]

Junjie Zhang, Shenzhou Zheng, Chunyan Zuo. $ W^{2, p} $-regularity for asymptotically regular fully nonlinear elliptic and parabolic equations with oblique boundary values. Discrete & Continuous Dynamical Systems - S, 2021, 14 (9) : 3305-3318. doi: 10.3934/dcdss.2021080
[15]

Luisa Fattorusso, Antonio Tarsia. Regularity in Campanato spaces for solutions of fully nonlinear elliptic systems. Discrete & Continuous Dynamical Systems, 2011, 31 (4) : 1307-1323. doi: 10.3934/dcds.2011.31.1307
[16]

Fabio Camilli, Claudio Marchi. On the convergence rate in multiscale homogenization of fully nonlinear elliptic problems. Networks & Heterogeneous Media, 2011, 6 (1) : 61-75. doi: 10.3934/nhm.2011.6.61
[17]

Pablo Blanc. A lower bound for the principal eigenvalue of fully nonlinear elliptic operators. Communications on Pure & Applied Analysis, 2020, 19 (7) : 3613-3623. doi: 10.3934/cpaa.2020158
[18]

Robert Jensen, Andrzej Świech. Uniqueness and existence of maximal and minimal solutions of fully nonlinear elliptic PDE. Communications on Pure & Applied Analysis, 2005, 4 (1) : 199-207. doi: 10.3934/cpaa.2005.4.187
[19]

Zhaoli Liu, Jiabao Su. Solutions of some nonlinear elliptic problems with perturbation terms of arbitrary growth. Discrete & Continuous Dynamical Systems, 2004, 10 (3) : 617-634. doi: 10.3934/dcds.2004.10.617
[20]

A. Rodríguez-Bernal. Perturbation of the exponential type of linear nonautonomous parabolic equations and applications to nonlinear equations. Discrete & Continuous Dynamical Systems, 2009, 25 (3) : 1003-1032. doi: 10.3934/dcds.2009.25.1003

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (70)
  • HTML views (0)
  • Cited by (48)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy