Weakly nonlinear hyperbolic differential equation of the second order in Hilbert space

We consider nonlinear perturbations of the hyperbolic equation in the Hilbert space. Necessary and sufficient conditions for the existence of solutions of boundary-value problem for the corresponding equation and iterative procedures for their finding are obtained in the case when the operator in linear part of the problem hasn't inverse and can have nonclosed set of values. As an application we consider boundary-value problem for van der Pol equation in a separable Hilbert space.

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Publication Details

Journal
Topological Methods in Nonlinear Analysis
Published
2024-09-15
DOI
https://doi.org/10.12775/tmna.2023.056
Primary Topic
Differential Equations and Boundary Problems
Type
article
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article

Weakly nonlinear hyperbolic differential equation of the second order in Hilbert space

O. O. Pokutnyi
Topological Methods in Nonlinear Analysis
Differential Equations and Boundary Problems
article

Weakly nonlinear hyperbolic differential equation of the second order in Hilbert space

O. O. Pokutnyi
article en

Abstract

We consider nonlinear perturbations of the hyperbolic equation in the Hilbert space. Necessary and sufficient conditions for the existence of solutions of boundary-value problem for the corresponding equation and iterative procedures for their finding are obtained in the case when the operator in linear part of the problem hasn't inverse and can have nonclosed set of values. As an application we consider boundary-value problem for van der Pol equation in a separable Hilbert space.

Topological Methods in Nonlinear Analysis
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Differential Equations and Boundary Problems
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Weakly nonlinear hyperbolic differential equation of the second order in Hilbert space — O. O. Pokutnyi · Topological Methods in Nonlinear Analysis (2024) | TGRS Research Map | TGRS