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Existence of periodic solutions for second-order neutral differential equations. (English) Zbl 1075.34065

Summary: By means of variational structure and critical point theory, we study the existence of periodic solutions for the second-order neutral differential equation \[ (p(t) x' (t - \tau ))' + f(t, x(t), x(t-\tau ), x(t-2\tau) ) = g(t),\quad x(0) = x(2k\tau), x'(0) = x'(2k\tau), \] where \(k\) is a given positive integer and \(\tau\) is a positive number.

MSC:

34K13 Periodic solutions to functional-differential equations
34K40 Neutral functional-differential equations
47J30 Variational methods involving nonlinear operators
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