In this paper, for the first order Hamiltonian systemsand the second order Hamiltonian systemswith the aids of variational methods, some existence results are obtained for subharmonic solution of local coercive sublinear Hamiltonian systems (HSl) and periodic solution of nonquadratic Hamiltonian systems (HS2).
Using the Rabinowitz′s saddle point theorem and Ambrosetti-Rabinowitz′s mountain Pass theorem and the morse index extimates of the corresponding critical points,we prove the existence of the subharmonic solution with prescribed minimal period about two classes of nonautonomus Hamiltionian systems
The existence of harmonic solution and infinitely many subharmonic solutions for Duffing equation x″+g(x)=p(t) are proved. In the Duffing equation, g(x) is an odd function and is satisfied with g′(x)> 0 and g(x)=a> 0.The continuous 2π-periodic function, namely p(t) satisfied: |p(t)|
Secondly, we discuss the existence of periodic solutions and sub-harmonic solutions of the above class of subquadratic higher-order difference equations being under the condition of positive-definited or negative-definited matrix by using minimax method.
Based on the successor map and a generalized version of the Poincare-Birkhoff twist theorem, we establish the existence of infinitely many subharmonics for a class of strongly asymmetric Duffing equations.
This approach is used for the numerical construction of subharmonic solutions in the case when the oscillator passes to chaos through a sequence of period-multiplying bifurcations.
We study the regular Hopf bifurcation and singular Hopf bifurcation from a basic equilibrium, and show the existence of the subharmonic solutions by using the averaging method and perturbed methods and bifurcation equations.
We provide sufficient conditions for the existence and multiplicity of subharmonic solutions for Duffing's equations with jumping nonlinearities.
Existence of periodic and subharmonic solutions for second-order superlinear difference equations
By critical point theory, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for difference equations.
The purplose of this paper is to prove the existence of intinitcly many subharmomic solutions of sub-linear Duffing equation.
This paper is to consider subharmornic solutions for a class of nonautonomous second order systems. the main result is that, under some suitable assumptions, there exists a sequence of periodic solutions of the systems such that the minimal periods are at most finitely same each other.