On state dependent non-local conditions |
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| Institution: | 1. Departamento de Computação e Matemática, Faculdade de Filosofia Ciências e Letras de Ribeirão Preto Universidade de São Paulo, CEP 14040-901 Ribeirão Preto, SP, Brazil;2. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland |
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| Abstract: | We introduce a new type of non-local conditions, which we call state dependent non-local conditions, and we study existence and uniqueness of solutions for abstract differential equation subjected to this class of conditions. The non-local condition proposed generalizes several types of non-local conditions studied in the literature. Some examples are given to illustrate our theory. |
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| Keywords: | Non-local conditions Mild solution Strict solutions Analytic semigroup |
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