Existence and multiplicity results for periodic solutions of superquadratic hamiltonian systems where the potential changes sign

1995 ◽  
Vol 2 (1) ◽  
pp. 35-61 ◽  
Author(s):  
Mario Girardi ◽  
Michele Matzeu
Keyword(s):  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Multiplicity Results ◽  
Existence And Multiplicity

PERIODIC SOLUTIONS FOR SINGULAR PERTURBATIONS OF THE SINGULAR ϕ-LAPLACIAN OPERATOR

2013 ◽  
Vol 15 (04) ◽  
pp. 1250063 ◽  
Author(s):  
CRISTIAN BEREANU ◽  
DANA GHEORGHE ◽  
MANUEL ZAMORA
Keyword(s):  
Periodic Solutions ◽  
Nonlinear Elasticity ◽  
Singular Perturbations ◽  
Continuous Functions ◽  
Lower And Upper Solutions ◽  
Laplacian Operator ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Periodic Problems ◽  
Singular Nonlinearities

In this paper, using Leray–Schauder degree arguments and the method of lower and upper solutions, we give existence and multiplicity results for periodic problems with singular nonlinearities of the type [Formula: see text] where r, n, e : [0, T] → ℝ are continuous functions and λ > 0. We also consider some singular nonlinearities arising in nonlinear elasticity or of Rayleigh–Plesset type.

Existence and multiplicity of periodic solutions to differential equations with attractive singularities

2021 ◽  
pp. 1-26
Author(s):  
José Godoy ◽  
Robert Hakl ◽  
Xingchen Yu
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Topological Degree ◽  
A Priori ◽  
New Method ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Upper And Lower Functions

The existence and multiplicity of T-periodic solutions to a class of differential equations with attractive singularities at the origin are investigated in the paper. The approach is based on a new method of construction of strict upper and lower functions. The multiplicity results of Ambrosetti–Prodi type are established using a priori estimates and certain properties of topological degree.

scholarly journals A systematic approach to nonresonance conditions for periodically forced planar Hamiltonian systems

2021 ◽  
Author(s):  
Christian Fabry ◽  
Alessandro Fonda
Keyword(s):  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Systematic Approach ◽  
General Setting ◽  
Differential Systems ◽  
Periodic Perturbations ◽  
Existence And Multiplicity

AbstractIn the first part of the paper we consider periodic perturbations of some planar Hamiltonian systems. In a general setting, we detect conditions ensuring the existence and multiplicity of periodic solutions. In the second part, the same ideas are used to deal with some more general planar differential systems.

Sign in / Sign up

Export Citation Format

Share Document