A singular periodic Ambrosetti–Prodi problem of Rayleigh equations without coercivity conditions.

In this paper, we use the Leray–Schauder degree theory to study the following singular periodic problems: x ″ + f (x ′) + g (t , x) = s , x (0) − x (T) = 0 = x ′ (0) − x ′ (T) , where f : ℝ → ℝ is a continuous function with f (0) = 0 , function g : ℝ / T ℤ × ℝ + → ℝ is continuous with an attractive singularity at the origin, and s is a constant. We consider the case where the friction term f satisfies a local superlinear growth condition but not necessarily of the Nagumo type, and function g does not need to satisfy coercivity conditions. An Ambrosetti–Prodi type result is obtained. [ABSTRACT FROM AUTHOR]