Inverse bifurcation problems for diffusive logistic equation of population dynamics

We consider the nonlinear eigenvalue problem arising in population dynamics:−u″(t)+f(u(t))=λu(t),u(t)>0,t∈I:=(0,1),u(0)=u(1)=0, where λ>0 is a parameter, f(u)=up+g(u) (p>1) and g(u) is assumed to be an unknown nonlinear term. The purpose of this paper is to study the inverse bifurcation problem in L1-framework. More precisely, we suppose that g(u) has compact support in [0,∞), and the precise global behavior of the L1-bifurcation curve of the equation is given. Then we show that g(u)≡0.