Affiliations: Department of Technical Mathematics and Informatics, University of Technology, Delft, The Netherlands E-mail: [email protected] | Departamento de Matemática, Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile E-mail: [email protected] | Centro de Modelamiento Matemático, Universidad de Chile, Casilla 170, Correo 3, Santiago, Chile E-mail: [email protected] | Departamento de Ingeniería Matemática, FCFM, Universidad de Chile, Casilla 170, Correo 3, Santiago, Chile E-mail: [email protected]
Abstract: We give a new region of existence of solutions to the superhomogeneous Dirichlet problem \begin{equation}\begin{array}{l}-\Delta_{p}u=v^{\delta},\quad v>0\ \mbox{in}\ B,\\-\Delta_{q}v=u^{\mu},\quad u>0\ \mbox{in}\ B,\\u=v=0\quad\mbox{on}\ \curpartial B,\end{array}\label{(S_R)}\end{equation} where B is the ball of radius R>0 centered at the origin in $\mathbb {R}^{N}$. Here δ,μ>0 and Δmu=div(|∇u|m−2∇u) is the m-Laplacian operator for m>1.
