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Weak singularities may help periodic solutions to exist. (English) Zbl 1116.34036

There are given conditions for the existence of a positive T-periodic solution of the equation
\[ x''+ a(t)x= f(t,x)+ c(t), \]
under the assumption, that the equation
\[ x''+ a(t)x= 0 \]
is nonresonant, that the corresponding Green’s function is nonnegative and
\[ 0\leq f(x,t)\leq b(t)/x^\lambda,\qquad 0<\lambda< 1. \]

MSC:

34C25 Periodic solutions to ordinary differential equations
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