Existence, multiplicity, and dependence on a parameter for a periodic boundary value problem

The authors consider the boundary value problem{y″−ρ2y+λg(t)f(y)=0,0⩽t⩽2π,y(0)=y(2π),y′(0)=y′(2π). Under different combinations of superlinearity and sublinearity of the function f, various existence, multiplicity, and nonexistence results for positive solutions are derived in terms of different values of λ. The uniqueness of solutions and the dependence of solutions on the parameter λ are also studied. The results are illustrated with an example.