Search results for "Second order equation"
showing 6 items of 6 documents
Elliptic equations and maps of bounded length distortion
1988
On considere l'equation elliptique d'ordre 2: L(u)=Σ i,f=1 n ∂ 1 (a ij ∂ ju )=0 ou les coefficients a ij sont des fonctions C 1 dans un domaine D de R n
Multiple periodic solutions for Hamiltonian systems with not coercive potential
2010
Under an appropriate oscillating behavior of the nonlinear term, the existence of infinitely many periodic solutions for a class of second order Hamiltonian systems is established. Moreover, the existence of two non-trivial periodic solutions for Hamiltonian systems with not coercive potential is obtained, and the existence of three periodic solutions for Hamiltonian systems with coercive potential is pointed out. The approach is based on critical point theorems. © 2009 Elsevier Inc. All rights reserved.
Multiplicity results for systems of asymptotically linear second order equations
2002
Abstract We prove the existence and multiplicity of solutions, with prescribed nodal properties, for a BVP associated with a system of asymptotically linear second order equations. The applicability of an abstract continuation theorem is ensured by upper and lower bounds on the number of zeros of each component of a solution.
Periodic solutions of a class of non-autonomous second order differential equations with discontinuous right-hand side
2012
Abstract The main goal of this paper is to discuss the existence of periodic solutions of the second order equation: y ″ + η sgn ( y ) = α sin ( β t ) with ( η , α , β ) ∈ R 3 η > 0 . We analyze the dynamics of such an equation around the origin which is a typical singularity of non-smooth dynamical systems. The main results consist in exhibiting conditions on the existence of typical periodic solutions that appear generically in such systems. We emphasize that the mechanism employed here is applicable to many more systems. In fact this work fits into a general program for understanding the dynamics of non-autonomous differential equations with discontinuous right-hand sides.
Three periodic solutions for perturbed second order Hamiltonian systems
2009
AbstractIn this paper we study the existence of three distinct solutions for the following problem−u¨+A(t)u=∇F(t,u)+λ∇G(t,u)a.e. in [0,T],u(T)−u(0)=u˙(T)−u˙(0)=0, where λ∈R, T is a real positive number, A:[0,T]→RN×N is a continuous map from the interval [0,T] to the set of N-order symmetric matrices. We propose sufficient conditions only on the potential F. More precisely, we assume that G satisfies only a usual growth condition which allows us to use a variational approach.
Infinitely many periodic solutions for a second-order nonautonomous system
2003
The existence of infinitely many solutions for a second-order nonautonoumous system was investigated. Some multiplicity results for problem (P) under very different assumptions on the potential G were established. It was shown that infinitely many solutions follow from a variational principle by B. Ricceri.