Existence results for a linear equation with reflection,non-constant coefficient and periodic boundary conditions |
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Authors: | Alberto Cabada F Adrián F Tojo |
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Institution: | Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, Spain |
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Abstract: | This work is devoted to the study of first order linear problems with involution and periodic boundary value conditions. We first prove a correspondence between a large set of such problems with different involutions to later focus our attention to the case of the reflection. We study then different cases for which a Green?s function can be obtained explicitly and derive several results in order to obtain information about its sign. Once the sign is known, maximum and anti-maximum principles follow. We end this work with more general existence and uniqueness of solution results. |
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Keywords: | Equations with involutions Equations with reflection Green?s functions Maximum principles Comparison principles Periodic conditions |
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