We consider power type nonlinear conjugation problem for analytic functions. Our main question is to make this problem well‐posed, i.e. to find such classes of functions in which this problem possesses a unique solution. These classes are those with prescribed collections of zeros in the domains and/or on their boundaries.
Analizinių funkcijų netiesinio sujungimo kraštinio uždavinio korektiškumas
Santrauka. Nagrinėjamas analizinių funkcijų netiesinio sujungimo kraštinis uždavinys. Analizuojami laipsninio tipo netiesiškumai. Pagrindinis darbo tikslas yra korektiškai suformuluoti uždavinį, t.y. rasti tokių funkcijų klasę, kurioje šis uždavinys turi vienintelį sprendinį. Parodyta, kad tokią funkcijų klasę sudaro funkcijos su iš anksto užduota nulių aibe srityje ir/arba ant jos kontūro.
Rogosin, S. V. (2000). On well‐posedness of nonlinear conjugation boundary value problem for analytic functions. Mathematical Modelling and Analysis, 5(1), 153-163. https://doi.org/10.3846/13926292.2000.9637138
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