Lq -inverse spectral problems for semilinear Sturm–Liouville problems

We consider the bifurcation problem −u″(t)+f(u(t))=λu(t),u(t)>0,t∈I≔(0,1),u(0)=u(1)=0−u″(t)+f(u(t))=λu(t),u(t)>0,t∈I≔(0,1),u(0)=u(1)=0, where λ>0λ>0 is a positive parameter. We determine the nonlinear term f(u)f(u) by the asymptotic behavior of the bifurcation curve of the positive solutions in R+×Lq(I), where 1≤q<∞1≤q<∞.