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 ) ) = λ u ( t ) , u ( t ) > 0 , t ∈ I : = ( 0 , 1 ) , u ( 0 ) = u ( 1 ) = 0 , where λ > 0 is a parameter, f ( u ) = u p + 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 L 1 -framework. More precisely, we suppose that g ( u ) has compact support in [ 0 , ∞ ) , and the precise global behavior of the L 1 -bifurcation curve of the equation is given. Then we show that g ( u ) ≡ 0 .