Bifurcation Conditions for the Solutions of Weakly Perturbed Boundary-Value Problems for Operator Equations in Banach Spaces
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We establish the conditions of bifurcation of the solutions of weakly perturbed boundary-value problems for operator equations in Banach spaces from the point 𝜀 = 0. A convergent iterative procedure is proposed for the construction of solutions as parts of series in powers of 𝜀 with poles at the point 𝜀 = 0.
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- 1.V. F. Zhuravlev, “Weakly perturbed operator equations in Banach spaces,” Ukr. Mat. Zh., 69, No. 6, 751–764 (2017); English translation : Ukr. Math. J., 69, No. 6, 876–891 (2017).Google Scholar
- 2.S. G. Krein, Linear Equations in Banach Spaces [in Russian], Nauka, Moscow (1971).Google Scholar
- 3.I. Ts. Gokhberg and N. Ya. Krupnik, Introduction to the Theory of One-Dimensional Singular Integral Operators [in Russian], Shtiintsa, Kishinev (1973).Google Scholar
- 4.M. I. Vishik and L. A. Lyusternik, “Solution of some problems on perturbations in the case of matrices and self-adjoint and nonselfadjoint differential equations,” Usp. Mat. Nauk, 15, Issue 3, 3–80 (1960).Google Scholar
- 5.A. A. Boichuk, Constructive Methods for the Analysis of Boundary-Value Problems [in Russian], Naukova Dumka, Kiev (1990).Google Scholar
- 9.O. A. Boichuk and E. V. Panasenko, “Weakly perturbed boundary-value problems for differential equations in a Banach space,” Nelin. Kolyv., 13, No. 3, 291–304 (2010); English translation : Nonlin. Oscillat., 13, No. 3, 311–324 (2011).Google Scholar
- 10.A. Ya. Khelemskii, Lectures on Functional Analysis [in Russian], MTsNMO, Moscow (2004).Google Scholar
- 11.M. M. Popov, “Complementable spaces and some problems of the contemporary geometry of Banach spaces,” Mat. S’ohodni’07, Issue 13, 78–116 (2007).Google Scholar
- 12.A. A. Boichuk, V. F. Zhuravlev, and A. A. Pokutnyi, “Normally solvable operator equations in a Banach space,” Ukr. Mat. Zh., 65, No. 2, 163–174 (2013); English translation : Ukr. Math. J., 65, No. 2, 179–192 (2013).Google Scholar