We give new conditions for the study of existence of positive radial solutions for a system involving the Hessian operator. The solutions to be obtained are given by successive-approximation. Our interest is to improve the works that deal with such systems at the present and to give future directions of research related to this work for researchers.
Citation: Dragos-Patru Covei. A remark on the existence of positive radial solutions to a Hessian system[J]. AIMS Mathematics, 2021, 6(12): 14035-14043. doi: 10.3934/math.2021811
We give new conditions for the study of existence of positive radial solutions for a system involving the Hessian operator. The solutions to be obtained are given by successive-approximation. Our interest is to improve the works that deal with such systems at the present and to give future directions of research related to this work for researchers.
| [1] |
J. Bao, X. Ji, H. Li, Existence and nonexistence theorem for entire subsolutions of k-Yamabe type equations, J. Differ. Equations, 253 (2012), 2140–2160. doi: 10.1016/j.jde.2012.06.018. doi: 10.1016/j.jde.2012.06.018
|
| [2] |
D. P. Covei, A remark on the existence of entire large and bounded solutions to a ($k_{1}$ , $k_{2}$)-Hessian system with gradient term, Acta Math. Sin., $\textbf{33}$ (2017), 761-774. doi: 10.1007/s10114-017-6291-3. doi: 10.1007/s10114-017-6291-3
|
| [3] |
P. Delanoë, Radially symmetric boundary value problems for real and complex elliptic Monge-Ampère equations, J. Differ. Equations, 58 (1985), 318–344. doi: 10.1016/0022-0396(85)90003-8. doi: 10.1016/0022-0396(85)90003-8
|
| [4] |
T. Kusano, C. A. Swanson, Existence theorems for Monge-Ampère equations in $\mathbb{R}^{N}$, Hiroshima Math. J., 20 (1990), 643–650. doi: 10.32917/hmj/1206129054. doi: 10.32917/hmj/1206129054
|
| [5] |
A. V. Lair, Entire large solutions to semilinear elliptic systems, J. Math. Anal. Appl., 382 (2011), 324–333. doi: 10.1016/j.jmaa.2011.04.051. doi: 10.1016/j.jmaa.2011.04.051
|
| [6] |
X. Ji, J. Bao, Necessary and sufficient conditions on solvability for Hessian inequalities, Proc. Amer. Math. Soc., 138 (2010), 175–188. doi: 10.1090/S0002-9939-09-10032-1. doi: 10.1090/S0002-9939-09-10032-1
|
| [7] |
Z. Zhang, H. Liu, Existence of entire radial large solutions for a class of Monge-Ampère type equations and systems, Rocky Mt. J. Math., 50 (2020), 1893–1899. doi: 10.1216/rmj.2020.50.1893. doi: 10.1216/rmj.2020.50.1893
|
Dragos-Patru Covei. A remark on the existence of positive radial solutions to a Hessian system[J]. AIMS Mathematics, 2021, 6(12): 14035-14043. doi: 10.3934/math.2021811
DownLoad: