Periodic solutions of some second-order differential equations with desultorily sublinear nonlinearities Original Research Article

In this paper, we study the existence of periodic solutions of the Rayleigh equations x″+f(x′)+g(x)=e(t).x″+f(x′)+g(x)=e(t). Turn MathJax on The nonlinear term gg satisfies the following conditions: View the MathML sourcelim infx→+∞g(x)x⩽0, Turn MathJax on and View the MathML sourcelim infx→+∞,x∈Saxg′(x)g(x)>−∞, Turn MathJax on where aa is a non-negative constant, View the MathML sourceSa={x∈R+:g(x)>a} with supSa=+∞supSa=+∞ and ff satisfies the sublinear condition. Using the Leray–Schauder continuation theorem, we give sufficient conditions for the existence of periodic solutions of the given equations.