Krasnoselskii’s fixed point theorem can be applied to both linear and nonlinear differential equations with various boundary conditions by reformulating the boundary value problem as an operator equation in a Banach space. The differential operator associated with the problem is decomposed into the sum of a contraction operator and a compact operator, in accordance with the structure required by the theorem. For linear equations, this decomposition is often straightforward, while for nonlinear problems additional functional assumptions are imposed to ensure compactness and contraction. Depending on whether the boundary conditions are of Dirichlet, Neumann, or mixed type, the associated Green’s function or integral operator is used to establish the mapping properties needed to apply the theorem.