Weakly nonlinear hyperbolic differential equation of the second order in Hilbert space
DOI:
https://doi.org/10.12775/TMNA.2023.056Keywords
Boundary-value problem, nonlinear hyperbolic differential equation, van der Pol equation, Moore-Penrose pseudo-inverse matrixAbstract
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.References
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