1,721,064 research outputs found
Variational problems at resonance without monotonicity
No full textFonda Alessandro. Variational problems at resonance without mono-tonicity. In: Bulletin de la Classe des sciences, tome 74, 1988. pp. 54-63
Periodic Solutions of Hamiltonian Systems with Symmetries
No full textAfter a brief historical account, starting with the celebrated Poincaré–Birkhoff Theorem, we provide a multiplicity result for periodic solutions of some Hamiltonian systems whose Hamiltonian function H(t,x,y) is periodic in the space variables x, and even in the variables (t,y). Our result is based on a recent theorem by R. Ortega and the author, and it does not require any twist condition on the solutions of the system
Playing Around Resonance. An Invitation to the Search of Periodic Solutions for Second Order Ordinary Differential Equations
No full textThis book is an introduction to the problem of the existence of solutions to some type of semilinear boundary value problems. The aim of the book is to give the possibility to any good student to reach a research level in this field, starting from the basic knowledge of mathematical analysis which is usually acquired before graduation. To this aim, I will develop some tools which could be used to attack many different boundary value problems, arising from ordinary or partial differential equations. However, I have chosen to deal mainly with the periodic problem for a second-order scalar ordinary differential equation. One reason for this choice is that this apparently simple model already shows so many different aspects, and can be approached by such different techniques, that it seems the ideal starting point to the further understanding of more technical boundary value problems. Another reason comes, of course, from its intrinsic importance in the applications
Positively homogeneous hamiltonian systems in the plane
No full textI try to give a general description of the dynamics of the solutions for a planar hamiltonian system with positively homogeneous hamiltonian function and periodic forcing term. Most of the results obtained are already known in the special case of a scalar second-order differential equation with asymmetric nonlinearity
Existence and uniqueness of solutions for semilinear equations involving anti-selfadjoint operators
No full textWe consider the problem of the existence and uniqueness of solutions to a semilinear equation in a Hilbert space, of the type Lu = Nu, where the linear operator L is assumed to be anti-selfadjoint, and the nonlinear part N is controlled by two bounded selfadjoint operators A and B. As an example of application, we study the existence and uniqueness of periodic solutions for a system of transport equations. Precisely, we look for solutions which are periodic in each of their variables, the periods being determined by the forcing term
Topological degree and generalized asymmetric oscillators
No full textWe consider periodic perturbations of an
isochronous hamiltonian system in the plane, depending on a parameter,
which generalize the classical asymmetric oscillator. We compute the
associated topological degree, and consider situations where
large-amplitude periodic solutions can arise
Periodic solutions for a conservative system of differential equations with a singularity of repulsive type
No full textA Modern Introduction to Mathematical Analysis
No full textFeatures an original approach to the exponential and circular functions.
Explains all the main analysis theory in only 450 pages.
Presents the Kurzweil-Henstock integral
Generalizing the Lusternik–Schnirelmann critical point theorem
No full textWe provide a multiplicity result for critical points of a functional defined on the product of a compact manifold without boundary and a convex set, by assuming, for example, an avoiding rays condition at the boundary of that set. We then extend this result to an infinite-dimensional setting which well applies to the search of periodic solutions of pendulum-like equations
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