Bifurcation curves of positive steady-state solutions for a reaction-diffusion problem of lake eutrophication

We study exact multiplicity and bifurcation curves of positive solutions for a multiparameter Dirichlet problem{u″(x)+λ[a−bu+up1+up]=0,−11, a,b are positive dimensionless parameters, and λ>0 is a bifurcation parameter. For fixed p>1, assume that either 00 and (a,b) lies below the curveΓ1={(a,b):a(t)=tp[p−1−tp](tp+1)2,b(t)=ptp−1(tp+1)2,0