Mathematics and Statistics Vol. 6(1), pp. 9 - 15
DOI: 10.13189/ms.2018.060102
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Exponential Dichotomy and Bifurcation Conditions of Solutions of the Hamiltonian Operators Boundary Value Problems in the Hilbert Space

Pokutnyi Oleksandr ^*
Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev, 01004, Ukraine

ABSTRACT

Sufficient conditions for the existence of solutions for a weakly linear perturbed boundary value problem are obtained in the so called resonance (critical) case. Iterative process for finding solutions has been presented. Necessary and sufficient conditions of the existence of solutions, bounded solutions, generalized solutions and quasi solutions are obtained.

KEYWORDS
Bifurcation Conditions, Lyapunov Equation, Exponential Dichotomy, Vishik-Lyusternik Method

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Pokutnyi Oleksandr , "Exponential Dichotomy and Bifurcation Conditions of Solutions of the Hamiltonian Operators Boundary Value Problems in the Hilbert Space," Mathematics and Statistics, Vol. 6, No. 1, pp. 9 - 15, 2018. DOI: 10.13189/ms.2018.060102.

(b). APA Format:
Pokutnyi Oleksandr (2018). Exponential Dichotomy and Bifurcation Conditions of Solutions of the Hamiltonian Operators Boundary Value Problems in the Hilbert Space. Mathematics and Statistics, 6(1), 9 - 15. DOI: 10.13189/ms.2018.060102.