Weakly nonlinear hyperbolic differential equation of the second order in Hilbert space
Copyright policy )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.
Perturbations, asymptotics of solutions to ordinary differential equations, van der Pol equation, Abstract hyperbolic equations, Nonlinear differential equations in abstract spaces, Nonlocal and multipoint boundary value problems for ordinary differential equations, Perturbations of nonlinear operators, nonlinear hyperbolic differential equation, Transformation and reduction of ordinary differential equations and systems, normal forms, boundary-value problem
Perturbations, asymptotics of solutions to ordinary differential equations, van der Pol equation, Abstract hyperbolic equations, Nonlinear differential equations in abstract spaces, Nonlocal and multipoint boundary value problems for ordinary differential equations, Perturbations of nonlinear operators, nonlinear hyperbolic differential equation, Transformation and reduction of ordinary differential equations and systems, normal forms, boundary-value problem
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