Eventually vanishing solutions of a forced Liénard system (Q1047303)

The author proves the existence of non-trivial eventually vanishing solutions, that is, solutions which tend together with their derivatives to \(0\) as \(t \rightarrow \pm \infty \), of the Liénard equation \[ x''+f(x)x' + g(x) = p(t). \] The method of proof consists of solving the periodic problem on larger and larger intervals for a sequence of approximating equations and proving the convergence of the so obtained sequence of periodic functions to a solution of the original equation having the desired property.