nonuniqueness; time-periodical solutions; semilinear equation; irrational periods; dual variational method
The author examined non-zero $T$-periodic (in time) solutions for a semilinear beam equation under the condition that the period $T$ is an irrational multiple of the length. It is shown that for a.e. $T \in R^1$ (in the sense of the Lebesgue measure on $R^1$) the solutions do exist provided the right-hand side of the equation is sublinear.
 D. G. Costa M. Willem: Multiple critical points of invariant functional and applications. Séminaire de Mathématique 2-éme Semestre Université Catholique de Louvain.
 I. Ekeland R. Temam: Convex analysis and variational problems
. North-Holland Publishing Company 1976. MR 0463994
 N. Krylová O. Vejvoda: A linear and weakly nonlinear equation of a beam: the boundary value problem for free extremities and its periodic solutions
. Czechoslovak Math. J. 21 (1971), 535-566. MR 0289918