Author:
Gao Hongliang,Wang Liyuan,Li Jiemei
Abstract
<abstract><p>In this paper, we consider the existence of radial solutions to a $ k $-Hessian system in a general form. The existence of radial solutions is obtained under the assumptions that the nonlinearities in the given system satisfy $ k $-superlinear, $ k $-sublinear or $ k $-asymptotically linear at the origin and infinity, respectively. The results presented in this paper generalize some known results. Examples are given for the illustration of the main results.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference28 articles.
1. L. A. Caffarelli, L. Nirenberg, J. Spruck, The Dirichlet problem for nonlinear second order elliptic equations(Ⅲ): Functions of the eigenvalues of the Hessian, Acta. Math., 155 (1985), 261–301. http://doi.org/10.1007/bf02392544
2. X. J. Wang, The $k$-Hessian equation, In: Geometric analysis and PDEs, Heidelberg: Springer, 1977 (2009), 177–252. http://doi.org/10.1007/978-3-642-01674-5_5
3. Z. Zhang, K. Wang, Existence and non-existence of solutions for a class of Monge-Ampère equations, J. Differential Equations, 246 (2009), 2849–2875. https://doi.org/10.1016/j.jde.2009.01.004
4. J. Bao, H. Li, L. Zhang, Monge-Ampère equation on exterior domains, Calc. Var. Partial Differential Equations, 52 (2015), 39–63. https://doi.org/10.1007/s00526-013-0704-7
5. D. P. Covei, Solutions with radial symmetry for a semilinear elliptic system with weights, Appl. Math. Lett., 76 (2018), 187–194. https://doi.org/10.1016/j.aml.2017.09.003