Tadesse AbdiWubu Getahun2025-09-052025-09-052024-09https://etd.aau.edu.et/handle/123456789/7363In this thesis, given a bounded domain Ω⊂𝑅𝑛. we focus on the variational form ∫ Ω{𝛼∇𝑢⋅∇𝜙+𝑎𝑢𝜙}𝑑𝑥=∫ Ω𝑓𝜙𝑑𝑥,𝜙∈𝐻01(Ω) Of an elliptic problem, −𝛼Δ𝑢+𝑎(𝑥)𝑢=𝑓,𝑖𝑛 Ω With various conditions (Dirichlet, Neumann, and Robin) on boundary 𝜕Ω. We provide some general results on uniqueness and also find sub (supper)-solutions with in the frame work of variational setting.en-USElliptic ProblemsVariational formThesis