共查询到20条相似文献,搜索用时 31 毫秒
1.
《Nonlinear Analysis: Theory, Methods & Applications》2007,66(12):2277-2301
We study a piecewise linear system approximating the behaviour of a switched DC/DC converter. We give conditions for a unique limit cycle in our different cases and give examples of complicated phenomena that might occur. The stability of a state space trajectory controlled converter is addressed. 相似文献
2.
A. Laradji 《Journal of Differential Equations》2018,264(8):5480-5488
We provide necessary and sufficient conditions for which an nth-order linear differential equation has a general polynomial solution. We also give necessary conditions that can directly be ascertained from the coefficient functions of the equation. 相似文献
3.
Filippo Gazzola Raffaella Pavani 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6696-6711
We give strong theoretical and numerical evidence that solutions to some nonlinear fourth order ordinary differential equations blow up in finite time with infinitely many wild oscillations. We exhibit an explicit example where this phenomenon occurs. We discuss possible applications to biharmonic partial differential equations and to the suspension bridges model. In particular, we give a possible new explanation of the collapse of bridges. 相似文献
4.
Inverse spectral problems are considered for differential pencils with boundary conditions depending polynomially on the spectral parameter and with a finite number of transmission conditions. We give formulations of the associated inverse problems such as Titchmarsh–Weyl theorem, Hochstadt–Lieberman theorem and Mochizuki–Trooshin theorem, and prove corresponding uniqueness theorems. The obtained results are generalizations of the similar results for the classical Sturm–Liouville operator on a finite interval. 相似文献
5.
Götz Grammel 《Set-Valued Analysis》1996,4(4):361-374
We consider nonlinear, singularly perturbed differential inclusions and apply the averaging method in order to construct a limit differential inclusion for slow motion. The main approximation result states that the existence and regularity of the limit differential inclusion suffice to describe the limit behavior of the slow motion. We give explicit approximation rates for the uniform convergence on compact time intervals. The approach works under controllability or stability properties of fast motion. 相似文献
6.
Perturbation of the Drazin inverse for closed linear operators 总被引:2,自引:0,他引:2
We investigate the perturbation of the Drazin inverse of a closed linear operator recently introduced by second author and Tran, and derive explicit bounds for the perturbations under certain restrictions on the perturbing operators. We give applications to the solution of perturbed linear equations, to the asymptotic behaviour ofC
0-semigroups of linear operators, and to perturbed differential equations. As a special case of our results we recover recent perturbation theorems of Wei and Wang. 相似文献
7.
We give sufficient conditions for the existence of extremal solutions to discontinuous and functional differential equations with impulses. Our main results are new even for ordinary differential equations without impulses. 相似文献
8.
By means of the Cauchy matrix, we give sufficient conditions for the existence and exponential stability of almost periodic solutions and periodic solutions for the delay impulsive logarithmic population. 相似文献
9.
J. Papadopoulos 《Periodica Mathematica Hungarica》1985,16(4):281-285
The purpose of this paper is to give some conditions for a ring to be hyperbaluable by a totally ordered semigroup. In § 1 we give some preliminary definitions and results, and a bibliographical note. The theorem in § 2 provides a sufficient condition for hypervaluability. The theorem in § 3 provides a necessary and sufficient condition for hypervaluability. In § 4 we provide an example of a ring satisfying the conditions of theorem 2 and is therefore hypervaluable by a totally ordered semigroup. 相似文献
10.
We investigate systems of ordinary differential equations with a parameter. We show that under suitable assumptions on the systems the solutions are computable in the sense of recursive analysis. As an application we give a complete characterization of the recursively enumerable sets using Fourier coefficients of recursive analytic functions that are generated by differential equations and elementary operations. 相似文献
11.
We discuss the analysis of linear constant coefficient differential algebraic equations
on infinite dimensional Hilbert spaces. We give solution concepts and discuss solvability criteria which are mainly based
on Laplace transform. Furthermore, we investigate the decoupling of these systems motivated by the Kronecker normal form for
the finite dimensional case. Applications are given by the analysis of mixed systems of ordinary differential, partial differential
and differential algebraic equations. 相似文献
12.
We give a numerical approximation of the solution of a high-order nonlinear initial-value problem by making use of certain properties of an adequate Schauder basis. 相似文献
13.
Toshiki Naito Satoru Murakami Jong Son Shin Pham Huu Anh Ngoc 《Integral Equations and Operator Theory》2007,58(2):255-272
We first give a criterion for positivity of the solution semigroup of linear Volterra integro-differential systems. Then,
we offer some explicit conditions under which the solution of a positive linear Volterra system is exponentially stable or
(robustly) lies in L2[0,+∞).
The first and last author are supported by the Japan Society for Promotion of Science (JSPS) ID No. P 05049. 相似文献
14.
J. Sugie 《Applicable analysis》2013,92(1-3):217-227
This paper is concerned with the oscillatory behavior of the delay-differential equation X'(t)=F(t,xt) including the equations x'(t)=-a(t)x(t-r(t,x(t))), [display math001] as special cases.We give conditions for the existence of a nonoscillatory solution of (1) and criteria for the oscillation of all solutions of (1), aiming at extending or generalizing to (1) some of the recent oscillation and nonoscillation results for delay equations of the form x'(t)=-a(t)x(t-p)). 相似文献
15.
This paper is the second of a two-part series in which we review the properties of
the rotation number for a random family of linear non-autonomous Hamiltonian systems. In
Part I, we defined the rotation number for such a family and discussed its basic properties. Here
we define and study a complex quantity - the Floquet coefficient w - for such a family. The
rotation number is the imaginary part of w.
We derive a basic trace formula satisfied by w,
and give applications to Atkinson-type spectral problems. In particular we use w to discuss
the convergence properties of the Weyl M-functions,
the Kotani theory, and the gap-labelling phenomenon for these problems. 相似文献
16.
This paper is an elementary introduction to the concepts of variational iteration method. First, the main concepts in variational iteration method, such as general Lagrange multiplier, restricted variation, correction functional, are explained heuristically. Subsequently, the solution procedure is systematically addressed, in particular, for nonlinear oscillators. Particular attention is paid throughout the paper to give an intuitive grasp for the method. The main motivation is to put things together in a convenient form for later reference and systematic use. 相似文献
17.
We discuss the solvability of integral equations associated with initial value problems for a nonlinear differential equation of fractional order. The differential operator is the Caputo fractional derivative and the inhomogeneous term depends on the fractional derivative of lower orders. We obtain the existence of at least one solution for integral equations using the Leray–Schauder Nonlinear Alternative for several types of initial value problems. In addition, using the Banach contraction principle, we establish sufficient conditions for unique solutions. Our approach in obtaining integral equations is the “reduction” of the fractional order of the integro-differential equations based on certain semigroup properties of the Caputo operator. 相似文献
18.
Bernd Schmutzler 《Integral Equations and Operator Theory》1997,27(4):478-492
Homogeneous linear differential equations in Banach spaces are considered, which depend smoothly on a parameter. A fundamental system of solutions is generated by eigenvalues and eigenvectors of the corresponding operator pencil. The dependence on the parameter of these solutions in canonical form is, in general, not smooth because of branching eigenvalues. This means, the eigenvalues, their number and multiplicities may change in a nonsmooth way with respect to the parameter. We construct a new fundamental system depending smoothly on the parameter, wich can be represented by linear combinations of the solutions in canonical form. 相似文献
19.
20.
In this paper we discuss the perturbations of a general planar Filippov system with exactly one switching line. When the system has a limit cycle, we give a condition for its persistence; when the system has an annulus of periodic orbits, we give a condition under which limit cycles are bifurcated from the annulus. We also further discuss the stability and bifurcations of a nonhyperbolic limit cycle. When the system has an annulus of periodic orbits, we show via an example how the number of limit cycles bifurcated from the annulus is affected by the switching. 相似文献