Abstract:
The problems related to the problem of periodic solutions of the quasilinear
Euler-Bernoulli equation with homogeneous boundary conditions on the segment are
discussed. The asymptotic formulas of the corresponding Sturm-Liouville problem
for eigenfunctions and eigenvalues, as well as the conditions for the invertibility of
the differential operator of the equation, are obtained. For the quasilinear Euler-
Bernoulli equation, the conditions of existence, uniqueness, non-existence, and
countable solvability are obtained.
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