A mathematical model of suspension bridges
We prove the existence of weak T-periodic solutions for a nonlinear mathematical model associated with suspension bridges. Under further assumptions a regularity result is also given.
Asymptotic behaviour of the solvability set for pendulum-type equations with linear damping and homogeneous Dirichlet conditions.
Behavior of forced asymmetric oscillators at resonance.
Coupled string-beam equations as a model of suspension bridges
We consider nonlinearly coupled string-beam equations modelling time-periodic oscillations in suspension bridges. We prove the existence of a unique solution under suitable assumptions on certain parameters of the bridge.
Jumping nonlinearities and mathematical models of suspension bridge
Mathematical models of suspension bridges
In this work we try to explain various mathematical models describing the dynamical behaviour of suspension bridges such as the Tacoma Narrows bridge. Our attention is concentrated on the derivation of these models, an interpretation of particular parameters and on a discussion of their advantages and disadvantages. Our work should be a starting point for a qualitative study of dynamical structures of this type and that is why we have a closer look at the models, which have not been studied in literature...
Mathematical models of suspension bridges: existence of unique solutions
Nontrivial periodic solutions for strong resonance hamiltonian systems
On a class of forced nonlinear oscillators at resonance
Resonance with respect to the Fučík spectrum.
Rigorous numerical stability estimates for the existence of KAM tori in a forced pendulum
Small divisors and large multipliers
We study germs of singular holomorphic vector fields at the origin of of which the linear part is -resonant and which have a polynomial normal form. The formal normalizing diffeomorphism is usually divergent at the origin but there exists holomorphic diffeomorphisms in some “sectorial domains” which transform these vector fields into their normal form. In this article, we study the interplay between the small divisors phenomenon and the Gevrey character of the sectorial normalizing diffeomorphisms....
Метод осреднения для слабо нелинейных операторных уравнений