1,721,061 research outputs found
Multiplicity results for periodic solutions of second order ODEs with asymmetric nonlinearities
No full textMultiplicity of solutions of Dirichlet problems associated with second-order equations in R2
No full textWe study the existence of multiple solutions for a two-point boundary-value problem associated with a planar system of second-order ordinary differential equations by using a shooting technique. We consider asymptotically linear nonlinearities satisfying suitable sign conditions. Multiplicity is ensured by assumptions involving the Morse indices of the linearizations at zero and at infinit
Poincar é-Birkhoff fixed point theorem and periodic solutions of asymptotically linear planar Hamiltonian systems. (Turin Fortnight Lectures on Nonlinear Analysis (2001))
No full textChaos in periodically perturbed planar Hamiltonian systems using linked twist maps
No full textWe present a simple topological approach for the search of fixed points and the detection of chaotic dynamics for two-dimensional
maps satisfying a twist condition on linked annuli. Applications to planar Hamiltonian systems are given
Seismic behaviour of gravity load designed flush end-plate joints
No full textFlush end-plate (FEP) beam-to-column joints are commonly used for gravity load resisting parts in steel multi-storey buildings. However, in seismic resisting structures FEP joints should also provide rotation capacity consistent with the global structural displacements. The current version of EN1993-1-8 recommends a criterion aiming at controlling the thickness of the end-plate in order to avoid brittle failure of the connection, which has been developed for monotonic loading conditions assuming elastic-perfectly plastic behaviour of the connection's components in line with the theory of the component method. Hence, contrary to the design philosophy of the hierarchy of resistances implemented in EN1998-1, the over strength and the hardening of the plastic components are not directly accounted for. In light of these considerations, this paper describes and discusses the results obtained from parametric finite element simulations aiming at investigating the moment-rotation response of FEP joints under cyclic actions. The influence of bolt diameter, thickness of end-plate, number of bolt rows and shape of beam profile on the joint response is discussed and design requirements are proposed to enhance the ductility of the joint
Fixed points for planar maps with multiple twists, with application to nonlinear equations with indefinite weight
No full textIn this paper, we investigate the dynamical properties associated with planar maps which can be represented as a composition of twist maps together with expansive-contractive homeomorphisms. The class of maps we consider present some common features both with those arising in the context of the Poincaré-Birkhoff theorem and those studied in the theory of topological horseshoes. In our main theorems, we show that the multiplicity results of fixed points and periodic points typical of the Poincaré-Birkhoff theorem can be recovered and improved in our setting. In particular, we can avoid assuming area-preserving conditions and we also obtain higher multiplicity results in the case of multiple twists. Applications are given to periodic solutions for planar systems of non-autonomous ODEs with sign-indefinite weights, including the non-Hamiltonian case. The presence of complex dynamics is also discussed. This article is part of the theme issue 'Topological degree and fixed point theories in differential and difference equations'
Extinction or coexistence in periodic kolmogorov systems of competitive type
Full text linkWe study a periodic Kolmogorov system describing two species nonlinear competition. We discuss coexistence and extinction of one or both species, and describe the domain of attraction of nontrivial periodic solutions in the axes, under conditions that generalise Gopalsamy conditions. Finally, we apply our results to a model of microbial growth and to a model of phyto- plankton competition under the effect of toxins
Connected branches of initial points for asymptotic BVPs, with application to heteroclinic and homoclinic solutions
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