# Article

Full entry | PDF   (0.9 MB)
Keywords:
nonuniqueness; time-periodical solutions; semilinear equation; irrational periods; dual variational method
Summary:
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.
References:
[1] J. M. Coron: Periodic solutions of a nonlinear wave equation without assumption of monotonicity. Math. Ann. 262 (1983), 273-285. DOI 10.1007/BF01455317 | MR 0690201 | Zbl 0489.35061
[2] D. G. Costa M. Willem: Multiple critical points of invariant functional and applications. Séminaire de Mathématique 2-éme Semestre Université Catholique de Louvain.
[3] I. Ekeland R. Temam: Convex analysis and variational problems. North-Holland Publishing Company 1976. MR 0463994
[4] 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

Partner of