Solution Of Nonlinear Integro-differential Equations Research Articles

Best Lp approximate solutions of nonlinear integrodifferential equations

In this paper best L p approximate solutions are shown to exist for a wide class of integrodifferential equations. Using approximation theory techniques, a local existence theorem for solutions is established, and the convergence of the best approximate solutions to a solution is shown.

Existence and boundedness of solutions of abstract nonlinear integrodifferential equations of nonconvolution type

Existence and boundedness theorems are given for solutions of nonlinear integrodifferential equations of type d dt u(t) + Bu(t) + ∝ 0 t a(t, s) Au(s) ds ϵ f(t) (t > 0) , (1.1) u(0) = u 0, Here A and B are nonlinear, possibly multivalued, operators on a Banach space W and a Hilbert space H, where W ⊆ H. The function f (0, ∞) → H and the kernel a( t, s): R × R → R are known functions. The results of this paper extend the results of Crandall, Londen, and Nohel [4] for equation (1.1). They assumed the kernel to be of the type a( t, s) = a( t − s). We relax this assumption and obtain similar results. Examples of kernels satisfying the conditions we require are given in section 4.

Hyperpolynomial approximation of solutions of nonlinear integro-differential equations

Hyperpolynomial approximation of solutions of nonlinear integro-differential equations

Computer investigation of nonlinear dynamical problems of plasma theory

Computer studies of certain dynamical problems of plasma theory and that of collective acceleration of ions which reduce to the solution of nonlinear integro-differential equations are presented.

Nouveaux problèmes concernant les équations intégro-différentielles non linéaires à plusieurs variables indépendantes. I

In the framework of recent results concerning mixed structures mathematical systems [9]-[10] and in particular hereditary systems in one and several variables [6], [11], an existence and uniqueness theorem concerning solutions of non-linear integro-differential equation in several variables with initial-integral data is presented, some stability theorems are established, and the construction of approximate solutions is succeeded.

Systèmes différentiels possédant la structure complexe. Existence, unicité, stabilité et approximation des solutions de certains systèmes intégro-différentiels non linéaires aux opérateurs différentiels ordinaires et hyperboliques

In the framework of recent results concerning mixed structures mathematical systems [2], [11] and in particular hereditary systems in one and several variables [12-14], an existence and uniqueness theorem concerning solutions of non-linear integro-differential equations with hyperbolic operators with initial-integral and ordinary differential operators data is presented, some stability theorems are established, and a construction of approximative solutions with corresponding errors evaluation is succeeded.

Bounds for solutions of nonlinear integrodifferential equations

Bounds for solutions of nonlinear integrodifferential equations