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Resonant Solutions And Turning Points In An Elliptic Problem With Oscillatory Boundary Conditions, Alfonso Castro, Rosa Pardo
Resonant Solutions And Turning Points In An Elliptic Problem With Oscillatory Boundary Conditions, Alfonso Castro, Rosa Pardo
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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.