Analysis With Applications Pdf __full__ — Linear And Nonlinear Functional

Linear Poisson equation: solvable via Lax–Milgram in H1_0(Ω), spectral expansions, and regularity theory. Nonlinear counterpart (−Δu + f(u) = g) requires variational formulation, critical point or monotone-operator techniques; solutions may be multiple and require delicate a priori estimates.