相关论文: Higher order analysis on the existence of periodic…
We study the spectra for a class of differential operators with asymptotically constant coefficients.These operators widely arise as the linearizations of nonlinear partial differential equations about patterns or nonlinear waves. We…
We present a generalized notion of degree for rotating solutions of planar systems. We prove a formula for the relation of such degree with the classical use of Brouwer's degree and obtain a twist theorem for the existence of periodic…
The averaging theory has been extensively employed for studying periodic solutions of smooth and nonsmooth differential systems. Here, we extend the averaging theory for studying periodic solutions a class of regularly perturbed…
We show that a problem on minimal periods of solutions of Lipschitz functional differential equations is closely related to the unique solvability of the periodic problem for linear functional differential equations. Sharp bounds for…
In this letter we apply a method recently devised in \cite{aapla03} to find precise approximate solutions to a certain class of nonlinear differential equations. The analysis carried out in \cite{aapla03} is refined and results of much…
Using Mawhin's coincidence degree theory, we obtain some new continuation theorems which are designed to have as a natural application the study of the periodic problem for cyclic feedback type systems. We also discuss some examples of…
In the paper we provide the construction of a coincidence degree being a homotopy invariant detecting the existence of solutions of equations or inclusions of the form $Ax\in F(x)$, $x\in U$, where $A\colon D(A)\multimap E$ is an…
We study the set of $T$-periodic solutions of a class of $T$-periodically perturbed coupled and nonautonomous differential equations on manifolds. By using degree-theoretic methods we obtain a global continuation result for the $T$-periodic…
There is studied problem on existence of solutions to non-homogeneous differential equation of higher even order. Similar problem arises while studying soliton and soliton-like solutions to partial differential equations of integrable type.…
We apply the averaging theory of high order for computing the limit cycles of discontinuous piecewise quadratic and cubic polynomial perturbations of a linear center. These discontinuous piecewise differential systems are formed by two…
In this paper, we extend the method proposed by Cochelin and Vergez [A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions, Journal of Sound and Vibration, 324 (2009) 243-262] to the case of…
We study existence and Lorentz regularity of distributional solutions to elliptic equations with either a convection or a drift first order term. The presence of such a term makes the problem not coercive. The main tools are pointwise…
We consider existence of periodic boundary value problems of nonlinear second order ordinary differential equations. Under certain half Lipschitzian type conditions several existence results are obtained. As applications positive periodic…
The main objective of this work is to develop, via Brower degree theory and regularization theory, a variation of the classical averaging method for detecting limit cycles of certain piecewise continuous dynamical systems. In fact, overall…
By applying a Mawhin's continuation theorem of coincidence degree theory, we establish sufficient conditions for the existence of a periodic solution for a class of impulsive neutral differential equations. The procedure adopted in this…
We prove the existence of periodic solutions in a class of nonlinear partial differential equations, including the nonlinear Schroedinger equation, the nonlinear wave equation, and the nonlinear beam equation, in higher dimension. Our…
Motivated by problems coming from different areas of the applied science we study the periodic solutions of the following differential system $$x'(t)=F_0(t,x)+\varepsilon F_1(t,x)+\varepsilon^2 R(t,x,\varepsilon),$$ when $F_0$, $F_1$, and…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
We establish higher order convergence rates in the theory of periodic homogenization of both linear and fully nonlinear uniformly elliptic equations of non-divergence form. The rates are achieved by involving higher order correctors which…
We develop a convergent variational perturbation theory for the frequency of time-periodic solutions of nonlinear dynamical systems. The power of the theory is illustrated by applying it to the Duffing oscillator.