Steady states for resource and sexual competition models with diffusions (Q415574)

The paper deals with the following elliptic system describing competing interaction between two species \[ \begin{cases} -\Delta u=u f(u,v) &\cr -\Delta v= vg(u,v) & \text{ in } \Omega\cr u=v=0 & \text{ on } \partial\Omega. \end{cases} \] It is studied the existence and nonexistence of positive solutions. In addition, when one of the coefficients of sexual competition is absent, the results for the multiplicity and stability of positive solutions are obtained. The methods employed are the upper-lower solution technique and the fixed point theory in a positive cone.