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On the existence of square-integrable solutions for systems with weak nonlinearity


The paper considers the problem of structural stability of systems under disturbance of coefficients having small L 2(ℝ)-norm. We derive conditions which guarantee that for every solution of the perturbed system there exists a solution of the original system which is close to the former in L 2(ℝ)-norm.

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Corresponding author

Correspondence to N. A. Begun.

Additional information

Original Russian Text © N.A. Begun, 2010, published in Vestnik Sankt-Peterburgskogo Universiteta. Seriya 1. Matematika, Mekhanika, Astronomiya, 2010, No. 2, pp. 71–79.

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Begun, N.A. On the existence of square-integrable solutions for systems with weak nonlinearity. Vestnik St.Petersb. Univ.Math. 43, 74–81 (2010).

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  • structural stability
  • hyperbolic system
  • linear system
  • heterogeneous system