Periodic solutions of quasilinear non-autonomous systems with impulses

The paper considers a system of differential equations with impulse perturbations at fixed moments in time of the form where x ? R ⁿ, ε is a small parameter, Sufficient conditions have been found for existence of the periodic solution of the given system in the critical and non-critical cases.     

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.     

Periodic solutions of second-order quasilinear hyperbolic equations

We study a periodic boundary-value problem for a quasilinear equation with the d'Alembert operator on the left-hand side and a nonlinear operator on the right-hand side and establish conditions under which the solution of the indicated problem is unique.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 10, pp. 1370–1375, October, 1995.     

Periodic non-autonomous second-order dynamical systems

We study the existence of periodic solutions for a second-order non-autonomous dynamical system. We give three sets of hypotheses which guarantee the existence of non-constant solutions. We were able to weaken the hypotheses considerably from those used previously for such systems. We employ a saddle point theorem using linking methods.     

非自治Liénard型系统的周期解

利用Mawhin的重合度理论及Brousk定理给出了一类非自治二阶微分系统周期解存在的一些充分条件,所获结果推广与扩展了有关文献的相应结果.     

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

     

Periodic solutions for a class of non-autonomous differential delay equations

By applying symplectic transformation, Floquet theory and some results in critical point theory, we establish the existence of periodic solutions for a class of non-autonomous differential delay equations, which can be changed to Hamiltonian systems.     

Periodic solutions of a quasilinear wave equation

We study the properties of wave operators satisfying the periodicity condition with respect to time and homogeneous boundary conditions of the third kind and of Dirichlet type. We prove the existence of a nontrivial periodic (in time) sine-Gordon solution with homogeneous boundary conditions of the third kind and of Dirichlet type. We obtain theorems on the existence of periodic solutions of a quasilinear wave equation with variable (in x) coefficients and a boundary condition of the third kind.     

Homoclinic solutions for a class of non-autonomous subquadratic second-order Hamiltonian systems

In this paper we consider the existence of homoclinic solutions for the following second-order non-autonomous Hamiltonian system:

(HS)     

Periodic and subharmonic solutions for a class of non-autonomous Hamiltonian systems

Some existence theorems are obtained for periodic and subharmonic solutions of a class of non-autonomous Hamiltonian systems. Our technical approach is based on a version of the Local Linking Theorem, and the Generalized Mountain Pass Theorem.     

Existence of homoclinic solutions for a class of second-order non-autonomous Hamiltonian systems

By using the variant version of Mountain Pass Theorem, the existence of homoclinic solutions for a class of second-order Hamiltonian systems is obtained. The result obtained generalizes and improves some known works.     

Periodic solutions of a quasilinear parabolic differential equation

This paper treats the quasilinear, parabolic boundary value problem $\text{u}{}_{\mathrm{xx}}\text{? u}{}_{\mathrm{t}}\text{= ??(x, t, u)}$u(0, t) = ?₁(t); u(l, t) = ?₂(t) on an infinite strip $\text{{(x, t) ¦ 0 < x < l, ?∞ < t < ∞}}$ with the functions $\text{?(x, t, u), ?}{}_1\text{(t), ?}{}_2\text{(t)}$ being periodic in t. The major theorem of the paper gives sufficient conditions on $\text{?(x, t, u)}$ for this problem to have a periodic solution u(x, t) which may be constructed by successive approximations with an integral operator. Some corollaries to this theorem offer more explicit conditions on $\text{?(x, t, u)}$ and indicate a method for determining the initial estimate at which the iteration may begin.     

Periodic solutions of the higher-dimensional non-autonomous systems

In this paper, the new existence theorem, unique theorem of periodic solution of the periodic system

and new stationary oscillation theorem of the periodic system

are derived by using functional analysis method, algebraic method and the new estimated formulas of solution of the homogenous linear system. Our results extend and improve some main results related to references. In addition, these criteria are of great interest in many applications such as computation.     

Periodic orbits of a one-dimensional non-autonomous Hamiltonian system

In this paper we study the properties of the periodic orbits of with x∈S¹ and a T₀ periodic potential. Called the frequency of windings of an orbit in S¹ we show that exists an infinite number of periodic solutions with a given ρ. We give a lower bound on the number of periodic orbits with a given period and ρ by means of the Morse theory.     

On oscillation of solutions of a nonautonomous quasilinear second-order equation

Sufficient conditions are obtained for the initial values of nontrivial oscillating (for t=ω) solutions of the nonautonomous quasilinear equation $$y'' \pm \lambda (t)y = F(t,y,y'),$$ wheret ∈ Δ=[a, ω[,-∞ <a < ω ≤+ ∞, λ(t) > 0, λ(t) ∈ C _Δ ⁽¹⁾ , |F((t,x,y))|≤L(t)(|x|+|y|)^1+α, L(t) ≥-0, α ∈ [0,+∞[, F: Δ × R² →R,F ∈C _Δ×R ²,R is the set of real numbers, and R² is the two-dimensional real Euclidean space.     

Asymptotics of solutions for a class of quasilinear second-order ordinary differential equations

We consider a class of quasilinear second-order ordinary differential equations that arise in the investigation of the problem on stationary convective mass transfer between a drop and a solid medium in the presence of a volume chemical reaction of power-law form [F(υ) ≡ υ ^ν ] for the case in which the Peclet number Pe and the rate constant k _υ of the volume chemical reaction tend to infinity. We prove the existence and uniqueness theorem for a boundary value problem and analyze asymptotic properties of the solution.