Infinitely many periodic solutions for a semilinear Euler-Bernoulli beam equation with variable coefficients

摘要

We consider the periodic solutions for a semilinear Euler-Bernoulli beam equation with variable coefficients, which is used to describe the infinitesimal undamped transverse vibration of a thin straight elastic beam in a plane. The presence of variable coefficients leads to the destruction of spectral separability, which implies a loss of compactness on the range. By translating the spectrum, we construct a suitable function space which plays a crucial role in this paper. On this basis, we establish a theorem on the existence of infinitely many periodic solutions for the nonlinearity satisfying sublinear growth. ? 2021 Elsevier B.V. All rights reserved.