Nonautonomous Second-order Systems Research Articles

Subharmonic solutions for nonautonomous sublinear second-order differential inclusions systems with [formula omitted]-Laplacian

An existence result is obtained for infinite subharmonic solutions of nonautonomous second-order sublinear differential inclusions systems with p -Laplacian by the minimax methods in the critical point theory.

Existence and multiplicity results for nonlinear nonautonomous second-order systems

In this paper we consider nonlinear periodic systems driven by the ordinary p -Laplacian and having a nonsmooth potential function. Under minimal and natural hypotheses on the nonsmooth potential and using variational methods based on the nonsmooth critical point theory we prove four existence theorems and a multiplicity theorem. We conclude the paper with an existence theorem for the scalar problem, in which the energy functional is indefinite (i.e. it is unbounded both above and below).

Periodic solutions for a quasilinear non-autonomous second-order system

In this paper, a quasilinear second-order system with periodic boundary conditions is studied. By the least action principle and classical theorems of variational calculus, existence results of periodic solutions are obtained.

A MULTIPLICITY THEOREM FOR A PERTURBED SECOND-ORDER NON-AUTONOMOUS SYSTEM

AbstractIn this paper we establish a multiplicity result for a second-order non-autonomous system. Using a variational principle of Ricceri we prove that if the set of global minima of a certain function has at least $k$ connected components, then our problem has at least $k$ periodic solutions. Moreover, the existence of one more solution is investigated through a mountain-pass-like argument.

Periodic solutions of non-autonomous second-order systems with a p-Laplacian

In this paper, we investigate non-autonomous second-order systems with a p-Laplacian and obtain existence results for periodic solutions with the dual least action principle.

On the existence of positive solution for second-order multi-points boundary value problems

Here we are concerned with the existence of positive solution for autonomous and nonautonomous second-order systems with multi-points boundary conditions. For nonautonomous systems we use the Schauder's fixed point theorem in a suitable Banach space, while for autonomous ones using fixed point theorems is usually useless because of the existence of trivial solution and for this we employed a method based on the implicit function theorem and topological degree. In order to verify the obtained results, we have considered some definite systems to verify the results numerically.

Existence and multiplicity of periodic solution for non-autonomous second-order systems with linear nonlinearity☆

Existence and multiplicity of periodic solution for non-autonomous second-order systems with linear nonlinearity☆

Existence and multiplicity of periodic solution for non-autonomous second-order systems with linear nonlinearity

The purpose of this paper is to study the existence and multiplicity of periodic solution for the following non-autonomous second-order systems: u ¨ ( t ) = ∇ F ( t , u ( t ) ) a . e . t ∈ [ 0 , T ] , u ( 0 ) - u ( T ) = u ˙ ( 0 ) - u ˙ ( T ) = 0 . Some new existence and multiplicity theorems are obtained by using the least action principle and the minimax method.

Saddle point characterization and multiplicity of periodic solutions of non-autonomous second-order systems

In the present paper, the non-autonomous second-order systems (1.1) u ̈ (t)= ∇F(t,u(t)), a.e. t∈[0,T], u(0)−u(T)= u ̇ (0)− u ̇ (T)=0, and (1.2λ) u ̈ (t)=β(t)u(t)+λ ∇F(t,u(t)), a.e. t∈[0,T], u(0)−u(T)= u ̇ (0)− u ̇ (T)=0, are studied and a existence result of periodic solutions with saddle point character and two new multiplicity results are obtained.

Periodic solutions for a class of non-autonomous second order systems

The purpose of this paper is to study the existence of periodic solutions of non-autonomous second-order systems u ̈ (t)=∇F t,u(t) , a.e. t∈[0,T], u(0)−u(T)= u ̇ (0)− u ̇ (T)=0. Some new existence theorems are obtained by the least action principle.

A note on periodic solutions of nonautonomous second-order systems

A multiplicity theorem is obtained for periodic solutions of nonautonomous second-order systems with partially periodic potentials by the minimax methods.

Infinitely many periodic solutions for a second-order nonautonomous system

In this paper we are interested in multiplicity results for a second-order nonautonomous system. Infinitely many solutions follow from a recent variational principle by B. Ricceri.

Periodic solutions for some nonautonomous second-order systems

Some existence theorems are obtained for periodic solutions of nonautonomous second-order systems by using the least action principle and the minimax methods.

Periodic Solutions of a Class of Non-autonomous Second-Order Systems

Some existence theorems are obtained by the least action principle for periodic solutions of nonautonomous second-order systems with a potential which is the sum of a subconvex function and a subquadratic function.

Periodic Solutions for Nonautonomous Second-Order Systems with Bounded Nonlinearity

Some existence and multiplicity theorems are obtained for periodic solutions of nonautonomous second-order systems with bounded nonlinearity by the minimax methods.

A linear inverse system approach in the context of chaotic communications

A chaotic signal masking scheme involving the inverse system approach which uses nonautonomous chaotic systems is presented. In this context, two simple second-order nonautonomous systems are studied to demonstrate how such forced systems can be used for private communication purposes. The two main difficulties arising in such applications are the chaos synchronization and the exact duplication of the transmitter's nonlinear parts at the receiving end also. It is shown that our approach overcomes such difficulties by making use of second-order forced systems. Examples of circuit implementations for the transmitter and the receiver subsystems are discussed to investigate different recovering techniques.

Periodic Solutions of Non-autonomous Second-Order Systems with γ-Quasisubadditive Potential

The existence of periodic solutions to non-autonomous second order systems with γ-quasisubadditive potential is proved with classical theorems of variational calculus.

Synthesis of optimally fast response control for second-order nonautonomous systems

Synthesis of optimally fast response control for second-order nonautonomous systems

Amplitude bounds for general nonautonomous second-order systems

An extension of the tracking-function method is described which may be used to obtain bounds on the response of general nonlinear, nonstationary, forced second-order systems. Two examples illustrate the facility with which the method may be applied, and the regions of practical stability which can be achieved.

A Procedure for Investigating the Liapunov Stability of Nonautonomous Linear Second-Order Systems

Utilizing Liapunov’s direct method a procedure is presented which generates sufficient conditions for the stability of the null solution of the nonautonomous differential equation x¨ + b(t)x˙ + a(t)x = 0. This procedure systematically leads to the construction of a Liapunov function for a given differential equation and thus eliminates the normally ad hoc nature of the direct method. Four examples illustrating the procedure are discussed.