Global bifurcation curves of nonlocal elliptic equations with oscillatory nonlinear term

We study the one-dimensional nonlocal elliptic equation of Kirchhoff type with oscillatory nonlinear term. We establish the precise asymptotic formulas for the bifurcation curves lambda(alpha) as alpha -> infinity and alpha -> 0, where alpha := vertical bar mu lambda vertical bar..infinity 8 and mu lambda is the solution associated with.lambda We show that the second term of.(a) is oscillatory as alpha -> infinity.