We consider the elliptic equation -Δu + 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.
© 2012 Pacific Journal of Mathematics
Castro, Alfonso and Pardo, Rosa, "Resonant Solutions and Turning Points in an Elliptic Problem with Oscillatory Boundary Conditions" (2012). All HMC Faculty Publications and Research. 483.