Results 281 to 290 of about 23,893 (314)

Evolution equations for a class of nonlinear operators

1983
This paper is concerned with the abstract nonlinear evolution equation \(U'+A(U)=0\), where A is a nonlinear operator in a Hilbert space H. A class of operators is introduced which generalizes the class of monotone operators. This class includes Lipschitz continuous perturbations of monotone operators, but extends well beyond such cases. The class also
DE GIORGI E, DEGIOVANNI M, MARINO, ANTONIO, TOSQUES M.   +3 more
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Parabolic equations with operator nonlinearity

Asian-European Journal of Mathematics
In this paper, we consider partial differential equations (PDE) of parabolic type with functional nonlinearity in the reaction summand. Our goal is to give the answer of the question if there exist a set of smooth functions satisfying the inequality [Formula: see text], where [Formula: see text] is a parabolic operator in the parabolic PDE with a ...
Saba Iftikhar, Alina Lazu, Tzanko Donchev, Nikolay Kitanov, Dimitar Kolev   +4 more
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SCATTERING OPERATOR FOR NONLINEAR KLEIN–GORDON EQUATIONS

Communications in Contemporary Mathematics, 2009
We prove the existence of the scattering operator in [Formula: see text] in the neighborhood of the origin for the nonlinear Klein–Gordon equation with a power nonlinearity [Formula: see text] where [Formula: see text]μ ∈ C, n=1,2.
Hayashi, Nakao, Naumkin, Pavel I.
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Nonlinear operator differential equations

Nonlinear Analysis: Theory, Methods & Applications, 1997
Under homogeneous initial conditions with respect to \(t\), the equation \[ (\partial^{2+ q}/\partial x^2\partial t^q)u(x,t)+ A(\partial^p/\partial t^p)u(x,t)+ B_0\int^t_0 u(x,\tau)u(x, t-\tau)d\tau= f(x,t) \] is considered as a differential equation with respect to \(x\) in the operator field of Mikusiński.
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A nonlinear operator functional equation of Volterra type

Applied Mathematics and Computation, 2004
This paper is concerned with the existence of monotonic solutions in \(L^{1}[0,+\infty)\) of the following Volterra integral equation \[ x(t)=\int_{0}^{t}k_{1}(t,s)f\left(s,\int_{0}^{s}k_{2}(s,\theta)x(\phi(\theta))\,d\theta\right)\,ds, \;\;t\geq 0. \] The proofs rely on the measure of noncompactness and the Darboux fixed point theorem.
Ahmed M. A. El-Sayed, Nagwa Sherif, Ibrahim Abou El-Farag   +2 more
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THE AVERAGING METHOD FOR WEAKLY NONLINEAR OPERATOR EQUATIONS

Mathematics of the USSR-Sbornik, 1989
The paper deals with the Cauchy problem for the differential equation \[ u_ t+Lu=\epsilon f[u],\quad u|_{t=0}=u_ 0;\quad u_{tt}+Lu=\epsilon f[u],\quad u|_{t=0}=u_ 0,\quad u_ t|_{t=0}=u_ 1. \] Here L is a linear operator, f[u] is a nonlinear perturbation, \(\epsilon\) is a small parameter.
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Generating operators for integrable nonlinear evolution equations

Journal of Soviet Mathematics, 1983
For linear problems which are associated with known, exactly integrable nonlinear evolution equations, one gives the corresponding integrodifferential Λ-operators. Relative to the expansions with respect to the elgenfunctions of Λ-operators, the method of the inverse scattering problem can be considered as the analog of the Fourier transform of linear ...
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ABSOLUTE STABILITY CRITERIA FOR NONLINEAR OPERATOR EQUATIONS

Mathematics of the USSR-Izvestiya, 1977
Conditions are obtained for the stability in the large of solutions of nonlinear equations of the form (1)Here is the infinitesimal generator of a semigroup of class , the maps and are bounded linear operators, and , and are (generally different) Hilbert spaces. The equations (1) describe a wide class of distributed parameter control systems.
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Operator Method of Solving Nonlinear Differential Equations

Lithuanian Mathematical Journal, 2002
The author shows how solutions of nonlinear differential equations can be represented by linear operators. A linear generalized operator and a multiplicative operator are constructed for this purpose. Some properties of these operators are presented as well illustrative examples related to solutions of ordinary and partial differential equations.
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A linearized energy-conservative scheme for two-dimensional nonlinear Schrödinger equation with wave operator

Applied Mathematics and Computation, 2021
Hongwei Li, Xu Guo
exaly