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On the existence and asymptotic behavior of large solutions for a semilinear elliptic problem in $R^n$
Uniqueness and existence of maximal and minimal solutions of fully nonlinear elliptic PDE
| 1. | Department of Mathematical Sciences, Loyola University of Chicago, 6325 North Sheridan Road, Chicago, IL 60626, United States |
| 2. | School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA 30332-0160, United States |
| [1] |
Shigeaki Koike, Andrzej Świech. Local maximum principle for $L^p$-viscosity solutions of fully nonlinear elliptic PDEs with unbounded coefficients. Communications on Pure & Applied Analysis, 2012, 11 (5) : 1897-1910. doi: 10.3934/cpaa.2012.11.1897 |
| [2] |
Francesca Da Lio. Remarks on the strong maximum principle for viscosity solutions to fully nonlinear parabolic equations. Communications on Pure & Applied Analysis, 2004, 3 (3) : 395-415. doi: 10.3934/cpaa.2004.3.395 |
| [3] |
Ibrahim Ekren, Jianfeng Zhang. Pseudo-Markovian viscosity solutions of fully nonlinear degenerate PPDEs. Probability, Uncertainty and Quantitative Risk, 2016, 1 (0) : 6-. doi: 10.1186/s41546-016-0010-3 |
| [4] |
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 |
| [5] |
Luisa Fattorusso, Antonio Tarsia. Regularity in Campanato spaces for solutions of fully nonlinear elliptic systems. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1307-1323. doi: 10.3934/dcds.2011.31.1307 |
| [6] |
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 |
| [7] |
Mariane Bourgoing. Viscosity solutions of fully nonlinear second order parabolic equations with $L^1$ dependence in time and Neumann boundary conditions. Discrete & Continuous Dynamical Systems - A, 2008, 21 (3) : 763-800. doi: 10.3934/dcds.2008.21.763 |
| [8] |
Italo Capuzzo Dolcetta, Antonio Vitolo. Glaeser's type gradient estimates for non-negative solutions of fully nonlinear elliptic equations. Discrete & Continuous Dynamical Systems - A, 2010, 28 (2) : 539-557. doi: 10.3934/dcds.2010.28.539 |
| [9] |
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 |
| [10] |
Mariane Bourgoing. Viscosity solutions of fully nonlinear second order parabolic equations with $L^1$ dependence in time and Neumann boundary conditions. Existence and applications to the level-set approach. Discrete & Continuous Dynamical Systems - A, 2008, 21 (4) : 1047-1069. doi: 10.3934/dcds.2008.21.1047 |
| [11] |
Meng Qu, Ping Li, Liu Yang. Symmetry and monotonicity of solutions for the fully nonlinear nonlocal equation. Communications on Pure & Applied Analysis, 2020, 19 (3) : 1337-1349. doi: 10.3934/cpaa.2020065 |
| [12] |
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 |
| [13] |
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 |
| [14] |
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 |
| [15] |
Chunhui Qiu, Rirong Yuan. On the Dirichlet problem for fully nonlinear elliptic equations on annuli of metric cones. Discrete & Continuous Dynamical Systems - A, 2017, 37 (11) : 5707-5730. doi: 10.3934/dcds.2017247 |
| [16] |
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 |
| [17] |
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 |
| [18] |
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 |
| [19] |
Xavier Cabré. Elliptic PDE's in probability and geometry: Symmetry and regularity of solutions. Discrete & Continuous Dynamical Systems - A, 2008, 20 (3) : 425-457. doi: 10.3934/dcds.2008.20.425 |
| [20] |
Paul H. Rabinowitz. A new variational characterization of spatially heteroclinic solutions of a semilinear elliptic PDE. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 507-515. doi: 10.3934/dcds.2004.10.507 |
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