$- dot(q) + L(t)q = V_q(t, q) + g(t)$
where $V : R \times R^N (\to) R$ is superquadratic and even in $q$ and $L(t)$ is a a symmetric, positive definite matrix. If $g(t) != 0$, in spite of the loss of symmetry a suitable perturbative method allows one to state the existence of infinitely many solutions of the problem.
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