Existence of positive periodic solutions to nonlinear second order differential equations Original Research Article

In this paper, we discuss the existence of positive periodic solutions to the nonlinear differential equation View the MathML sourceu″(t)+a(t)u(t)=f(t,u(t)),t∈R, Turn MathJax on where a:R→[0,+∞)a:R→[0,+∞) is an ωω-periodic continuous function with a(t)⁄≡0a(t)⁄≡0, f:R×[0,+∞)→[0,+∞)f:R×[0,+∞)→[0,+∞) is continuous and f(⋅,u):R→[0,+∞)f(⋅,u):R→[0,+∞) is also an ωω-periodic function for each u∈[0,+∞)u∈[0,+∞). Using the fixed point index theory in a cone, we get an essential existence result because of its involving the first positive eigenvalue of the linear equation with regard to the above equation.