Global bifurcation curves of nonlocal elliptic equations with oscillatory nonlinear term

Abstract

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 λ ( α ) as α → ∞ and α → 0 , where α := ‖ u λ ‖ ∞ and u λ is the solution associated with λ . We show that the second term of λ ( α ) is oscillatory as α → ∞ .