Resonant solutions and turning points in an elliptic problem with oscillatory boundary conditions
Alfonso Castro, Rosa Pardo San Gil · Pacific Journal of Mathematics · 2012
We consider the elliptic equation -u+u = 0 with nonlinear boundary conditions ∂ u/∂n = λu + g(λ, x, u), where the nonlinear term g is oscillatory and satisfies g(λ, x, s)/s → 0 as |s| → 0. We provide sufficient conditions on g for the existence of sequences of resonant solutions and turning points accumulating to zero.