A note on stability of solutions for abstract semilinear Dirichlet problems

• Autorzy: Galewski M
• Języki publikacji: EN

Abstrakty

EN

We provide stability results for the family Lκu=∇Fκ(u) where Lκ is positive definite and selfadjoint operator and ∇Fκ for κ=0,1,2,... is a gradient mapping. The abstract results obtained are applied to prove the stability and continuous dependence on parameters for the fourth order Dirichlet problems for ordinary differential equations with the differential operator depending on numerical parameters.

Słowa kluczowe

EN

abstract Dirichlet problem; dual variational method; stability; continuous dependence on parameters

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2006
• Tom: Vol. 12, nr 1
• Strony: 71--81
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Galewski M

• Faculty of Mathematics. University of Łódź, Banacha 22, 90-238 Łódź, Poland,

Bibliografia

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• [9] Walczak, S., On the continuous dependance on parameters of solutions of the Dirichlet problem. Part I. Coercive case; Part II. The case of saddle points, Acad. Roy. Belg. Bull. Cl. Sci. (6) 6 (1995), 247-273.
• [10] Walczak, S., Continuous dependance on pammeters and boundary data for nonlinear P.D.E. Coercive case, Differential Integral Equations 11 (1998), 35-46.