Geodesic
On the existence of free vibrations for a beam equation when the period is an irrational multiple of the length
Applications of Mathematics, Tome 33 (1988) no. 2, pp. 94-102.

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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.
DOI : 10.21136/AM.1988.104291
Classification : 35B10, 35K60, 35L70, 58E05, 73K12
Keywords: nonuniqueness; time-periodical solutions; semilinear equation; irrational periods; dual variational method 
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     title = {On the existence of free vibrations for a beam equation when the period is an irrational multiple of the length},
     journal = {Applications of Mathematics},
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Feireisl, Eduard. On the existence of free vibrations for a beam equation when the period is an irrational multiple of the length. Applications of Mathematics, Tome 33 (1988) no. 2, pp. 94-102. doi : 10.21136/AM.1988.104291. http://geodesic.mathdoc.fr/articles/10.21136/AM.1988.104291/

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