Uniqueness of excited states to −Δu + u−u3= 0 in three dimensions
Uniqueness of excited states to −Δu + u−u3= 0 in three dimensions
We prove the uniqueness of several excited states to the ODE ÿ(t)+ 2 t ẏ(t)+f (y(t)) = 0, y(0) = b, and ẏ(0) = 0 for the model nonlinearity f (y) = y 3 -y.The n-th excited state is a solution with exactly n zeros and which tends to 0 …