| MSC: | 35J60 | Nonlinear PDE of elliptic type |
| 35J65 | Nonlinear boundary value problems for linear elliptic PDE; boundary value problems for nonlinear elliptic PDE | |
| ZDM: | - | |
| CR: | - | |
| PACS: | - |
Abstract:
In this paper, we obtain some new results on the existence of non-negative solutions for systems of the form
\[
(-\Delta +q_i)u_i = \mu_i m_iu_i+\sum_{j=1;j\neq i}^n a_{ij} u_j +f_i(x,u_1,...,u_n) \mbox{ in } \mathbb{R}^N,\; i=1,...,n,
\]
where each of the $q_i$ are positive potentials satisfying $\lim_{|x|\rightarrow +\infty} q_i(x)=+\infty$, each of the $m_i$ are bounded positive weights, each of the $a_{ij}$, $i \neq j$, are bounded non-negative weights and each of the $\mu_i$ are real parameters. Depending upon the hypotheses on $f_i$, we obtain some new results by using sub- and super-solution methods and the Schauder Fixed Point Theorem.