Buy stability of solutions of differential equations in banach s translations of mathematical monographs on free shipping on qualified orders. On the ulam stability of a class of banach space valued. According to these results, the nonrectifiable attractivity on a finite interval of the zero solution of the twodimensional linear integrable differential systems with singular matrix. Strong solutions for differential equations in abstract spaces. Abstractthis paper is devoted to investigating the nonlinear stability properties of linear multistep methods for the solution to neutral delay differential equations in banach space. On the ulam stability of a class of banach space valued linear differential equations of second order article pdf available in advances in difference equations 20141 november 2014 with 15 reads. On the stability of solutions of certain linear set differential equations. A series of contractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations nfdes in banach spaces are obtained, which provide unified. The study of abstract evolution equations is usually performed in a framework of two or more banach spaces, see the semigroup approach of. A fixedpoint approach to the hyersulam stability of. Pdf stability of linear multistep methods for nonlinear. On firstorder ordinary differential equations in banach spaces by madeaha mabrouk alghanmi a this thesis submitted for the requirements of the degree of master of science mathematics differential equations supervised by dr.
A theory for a class of semilinear evolution equations in banach spaces is developed which when applied to certain parabolic partial differential equations with nonlinear terms in divergence form gives strong solutions even for nondifferentiable data. Daleckii and mg krein, stability of solutions of differential. Differential equations and their applications in russian, no. Absolute stability of the solutions of linear differential. Conditions are presented for the mean stability of stationary periodic solutions under small perturbation of the coefficients. Exponential stability for solutions of continuous and discrete abstract cauchy problems in banach spaces constantin buse, toka diagana, lan thanh nguyen, donal oregan abstract. Two approaches to numerically treating the neutral term are considered, which allow us to prove several results on numerical stability of linear multistep. In this paper, we first introduce the test problem classes with respect to the initial value problems of nonlinear stiff impulsive differential equations in banach spaces. In this paper, we study the existence and stability of solutions for a class of abstract functional difference equations described in the form in a banach space, the space of bounded sequences equipped with the norm on, and is a function defined on, whose values are bounded operators in. All of this machinery is developed to study the lipschitz stability of a nonlinear. Canonical differential equations contents note continued. We study the asymptotic behaviour on a finite interval of a class of linear nonautonomous singular differential equations in banach space by the nonintegrability of the first derivative of its solutions.
The connection between the exponential stability of the solutions of linear differential equations in space of multidimensional bounded vector sequences and the absolute asymptotic stability of the solutions of differential equations with several time lags is investigated. We establish the robustness of the exponential stability in infinitedimensional banach spaces, in the sense that the exponential stability for a given pseudolinear equation persists under sufficiently small perturbations. You might not require more time to spend to go to the books foundation as without difficulty as search for them. Know that ebook versions of most of our titles are still available and may be downloaded immediately after purchase. Stability of bounded solutions of differential equations with small parameter in a banach space m. Stability for functional differential equations with delay. Let x be a banach space and let c cr,0,x denote the space of continuous functions from r, 0 to x. On the stability and asymptotic behavior of solutions of.
Second order equations infinitedimensional analog of hills equation 6. Some information from the theory of bounded operators in banach spaces 9 16 the linear equation with a constant operator 69 76 the nonstationary linear equation. We prove the ulam stability of a class of banach space valued second order linear differential equations, where, with for each. The analytic and numerical stability of stiff impulsive. Stability problems in nonautonomous linear differential. If the order n is even we can use the green function technique as the following.
Stability of bounded solutions of differential equations. This result of alsina and ger has been generalized by takahasi et al. A characterization of the stability of a system of the banach space valued differential equations takeshimiura,go hirasawa,sinei takahasi andtakahiro hayata abstract. Pdf stability for functional differential equations with. Our notation follows that of hale 7 and travis and webb i. Representation of solutions and stability of linear. More precisely we consider the nonlinear banach space volterra integral equation. Stability of solutions of differential equations in banach spaces. Linear difference and differential equations with operator coefficients and random stationary periodic input are considered. Pdf semigroups and stability of nonautonomous differential. Stability analysis for systems of differential equations. It is important that the approximations generated by the method are themselves close to the true solution.
Nonautonomous differential equations in banach space and. Integrally small perturbations of semigroups and stability. In this paper the problem of convergence in norm of solutions of the nonlinear functional differential. On the stability problem of differential equations in the sense. Fixed point, differential equations, banach space, stability, measure of noncompactness cite this paper kisiolek, a. These keywords were added by machine and not by the authors. In a sequentially weakly complete banach space, if the dual operator of a linear operator a satisfies certain conditions, then the spectrum of any weakly almost periodic solution of the. Nontrivial solutions for a class of fractional differential equations with integral boundary conditions and a parameter in a banach space with lattice zhang, xingqiu and wang, lin, abstract and applied analysis, 2012. Introduction the class of equations considered in this work have the form 1 u. Alhuthali faculty of science king abdulaziz university jeddah saudi arabia rajab. Necessary and sufficient conditions for different types of stability are given in terms of spectral. I, and bx is the space of bounded linear operators. Pdf linear difference and differential equations with operator coefficients and.
Contractivity and exponential stability of solutions to. On firstorder ordinary differential equations in banach. Stability of solutions of differential equations in banach space cover image. Dyachenko, semigroups of generalized almostnegative type and stabilization of solutions of differential equations in a banach space, in. Acces pdf stability solutions differential equations banach this is likewise one of the factors by obtaining the soft documents of this stability solutions differential equations banach by online. Stability for linear volterra difference equations in. Some sufficient conditions for the stability and asymptotic stability of the systems are given. We study the local exponential stability of evolution difference systems with slowly varying coefficients and nonlinear perturbations. Pdf on the ulam stability of a class of banach space.
Semilinear functional differential equations in banach space. Differential equations 4 example steady state solution and stability yxy finding the steady state solution to yxy, and then determining the stability of the solution using a slope field. Differential equations in a banach space springerlink. Lyapunov transformation and stability of differential. New approaches to the study of stability of solutions of set differen. They proved in 18 that the hyersulam stability holds for the banach space valued differential equation y x. Lyapunov transformation and stability of differential equations in banach. Stability of solutions of differential equations in banach space. The existence of positive solutions for boundary value problem of nonlinear fractional differential equations chen, yanli and li. Representation of solutions and stability of linear differential difference equations in a banach space richard datko department of mathematics, georgetown university, tvashingto. In this paper we study the robustness of the stability in nonautonomous linear ordinary differential equations under integrally small perturbations in infinite dimensional banach spaces. Vainberg, branching of periodic solutions of autonomous systems and of differential equations in banach spaces, dokl. Existence of solutions to quasilinear differential.
A characterization of the stability of a system of the. Stability of linear multistep methods for nonlinear neutral delay differential equations in banach space. Existence of solutions to quasilinear differential equations in a banach space volume 15 issue 3 james r. Banach space, a is an operator valued function taking t into a bounded linear operator at acting on x. Stability of stationary and periodic solutions equations. This paper is devoted to investigating the nonlinear stability properties of linear multistep methods for the solution to neutral delay differential equations in banach space. Three, a theory of uniform asymptotic stability for linear delay differential equations in a hubert space is developed. Some applications are obtained to the case of rapidly oscillating perturbations, with arbitrarily small periods, showing that even in this case the stability is robust. Stability of stationary and periodic solutions equations in banach space. Physical stability of an equilibrium solution to a system of di erential equations addresses the behavior of solutions that start nearby the equilibrium solution. These results are applied to partial differential equations. Stability of linear multistep methods for nonlinear. For the ulam stability of some integral equations see and 21.
Horodnii ukrainian mathematical journal volume 55, pages 1071. Expansion of the logarithm of the monodromy operator in powers of a small parameter. The stability and asymptotic stability results of the analytic solution of the abovementioned problems are obtained. Two approaches to numerically treating the neutral term are considered, which allow us to prove several results on numerical stability of linear multistep methods. The aim of this paper is to prove the stability in the sense of hyersulamrassias of the banach space valued differential equation y. The theory of differential equations in banach spaces has provided. The ams bookstore is open, but rapid changes related to the spread of covid19 may cause delays in delivery services for print products. Stability of solutions of differential equations in banach space, by ju. Stability of solutions of differential equations in banach.
957 126 1073 313 1222 26 1435 107 1489 1520 1014 383 570 1263 1286 386 1206 1017 165 1270 527 1586 909 503 95 1580 338 8 356 730 158 920 561 41 502 1396 1049 887 91 1299 152 904