Browsing by Author "Wubu Getahun"

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    Elliptic Problems and the Variational form
    (Addis Ababa University, 2024-09) Wubu Getahun; Tadesse Abdi
    In this thesis, given a bounded domain Ī©āŠ‚š‘…š‘›. we focus on the variational form āˆ« Ī©{š›¼āˆ‡š‘¢ā‹…āˆ‡šœ™+š‘Žš‘¢šœ™}š‘‘š‘„=āˆ« Ī©š‘“šœ™š‘‘š‘„,šœ™āˆˆš»01(Ī©) Of an elliptic problem, āˆ’š›¼Ī”š‘¢+š‘Ž(š‘„)š‘¢=š‘“,š‘–š‘› Ī© With various conditions (Dirichlet, Neumann, and Robin) on boundary šœ•Ī©. We provide some general results on uniqueness and also find sub (supper)-solutions with in the frame work of variational setting.