Abstract
In this article we study existence and uniqueness of positive solutions for elliptic systems of the form $$ \begin{align} -\Delta v = &f(x,u) \quad \hbox{in} \quad \Omega \\ -\Delta u = & v^\beta \quad \hbox{in}\quad \Omega, \end{align} $$ with Dirichlet boundary condition on a bounded smooth domain in $\Bbb R^N$. The nonlinearity $f$ is assumed to have a sub-$\beta$ growth with $\beta>0$, that in case $f(x,u)=u^\alpha, \alpha>0$, corresponds to $\alpha\beta<1$. The results are also valid for a larger class of systems, including some infinite dimensional Hamiltonian Systems.
Citation
Patricio Felmer. Salomé Martínez. "Existence and uniqueness of positive solutions to certain differential systems." Adv. Differential Equations 3 (4) 575 - 593, 1998. https://doi.org/10.57262/ade/1366292564
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