The methods to solve some classes boundary value problems via the results in double controlled metric-like spaces
Решение некоторых классов граничных задач с помощью результатов, полученных в частично метрических пространствах с двойным контролем
DOI:
https://doi.org/10.21638/spbu10.2025.105Аннотация
В работе представлены методы решения граничных задач второго и четвертого порядков. Доказываются несколько новых теорем о неподвижной точке в частично метрических пространствах с двойным контролем. Вводится сжимающее отображение Gζ, которое действует в том же пространстве, дополнительно снабженное графом, связывающим его элементы, и выводятся результаты о неподвижной точке этого отображения. В качестве приложения полученные результаты используются для доказательства существования решений некоторых классов граничных задач второго и четвертого порядков.
Ключевые слова:
дифференциальные уравнения, неподвижная точка, теория графов, частично метрические пространства с двойным контролем
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