Continuous Dependence of the Singular Nonlinear Van der Pol Equation Solutions with Respect to the Boundary Conditions: Elements of p-regularity Theory

Author:

Medak BeataORCID,Tret’yakov Alexey A.ORCID

Abstract

AbstractThis paper studies the problem of the continuous dependence of Van der Pol equation solutions with respect to the boundary conditions. We provide a new approach for the existence of such solutions via p-regularity theory. Several existence theorems about continuous solutions are established.

Funder

Российский Фонд Фундаментальных Исследований

Russian Academy of Sciences

Ministerstwo Nauki i Szkolnictwa Wyższego

Publisher

Springer Science and Business Media LLC

Subject

Analysis

Reference11 articles.

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2. Brezhneva, O.A., Tret’yakov, A.A., Marsden, J.E.: Higher-order implicit function theorems and degenerate nonlinear boundary-value problems. Commun. Pure Appl. Anal. 7(2), 293–315 (2008)

3. Ioffe, A.D., Tihomirov, V.M.: Theory of Extremal Problems. North-Holland, Amsterdam (1979)

4. Izmailov, A.F., Tret’yakov, A.A.: Factor-Analysis of Nonlinear Mappings. Nauka, Moscow (1994). (in Russian)

5. Izmailov, A.F., Tret’yakov, A.A.: 2-Regular Solutions of Nonlinear Problems. Theory and Numerical Methods. Nauka, Moscow (1999). (in Russian)

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