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Variational methods for nonlinear operator equations

, 1976
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Solutions of Nonlinear Operator Equations

SIAM Journal on Mathematical Analysis, 1977
Some theorems concerning existence and uniqueness of zeros of operator polynomials are given. Under certain hypotheses we show the existence of complete pairs of zeros. A numerical example is given applying the theorems.
Lancaster, Peter, Rokne, Jon G.
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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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Corrected Operator Splitting for Nonlinear Parabolic Equations

SIAM Journal on Numerical Analysis, 2000
The paper concerns a corrected operator splitting method for solving nonlinear parabolic equations of convection-diffusion type. It is shown that the method generates a compact sequence of approximate solutions which converges to the solution of the problem.
Karlsen, Kenneth Hvistendahl, Risebro, Nils Henrik   +1 more
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Nonlinear equations with differentiable operators

1994
Let \( \mathfrak{D} \) be a topological space. Assume that F is an operator defined from \( \mathfrak{D} \) into \( \mathfrak{D} \), i.e., $$ F\left( \mathfrak{D} \right) \subseteq \mathfrak{D} $$ (1)
Victor Khatskevich, David Shoiykhet
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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 equations with holomorphic operators

1994
Throughout this chapter we will consider complex Banach spaces only. In this case, many local features related to the solvability of equations with operators that are differentiable in the complex sense, turn out to be global.
Victor Khatskevich, David Shoiykhet
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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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Nonlinear Operators, Fixed-Point Theorems, Nonlinear Equations

2015
In this article we discuss the solvability of some class of fully nonlinear equations, and equations with p-Laplacian in more general conditions by using a new approach given by Soltanov in Nonlinear Anal. 72:164–175, 2010 for studying the nonlinear continuous operator.
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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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