The Existence of Positive Solution of a Nonlinear Problem on Unit Circle

Abstract

We consider the following nonlinear problem u″x+λux+fx,u=0, x∈S1, (P) where S1 is a unit circle, λ∈ℝ is a parameter, and fx,u is a nonlinearity. By using the variational method, we obtain the existence of a positive solution to (P) for all λ∈ℝ. This phenomenon is different from the corresponding boundary value problem.