Nonlinear functional analysis is concerned with the study of nonlinear operators between vector spaces. It involves the study of nonlinear functionals, which are functions that assign a scalar value to each vector in a vector space, but do not preserve the operations of vector addition and scalar multiplication.
The title " Linear and Nonlinear Functional Analysis with Applications Nonlinear functional analysis is concerned with the study
Quick study plan (8 weeks, self-study) Week 1–2: Banach/Hilbert basics, Lp spaces, Riesz representation, Hahn–Banach. Week 3: Bounded linear operators, spectral basics, compact operators. Week 4: Lax–Milgram, weak solutions, Sobolev spaces, Poincaré inequality. Week 5: Fixed-point theorems, Schauder, Banach contraction, basic applications. Week 6: Monotone operators, Minty–Browder, variational inequalities. Week 7: Calculus of variations, direct method, Mountain Pass theorem. Week 8: Applications: elliptic & parabolic PDEs, one nonlinear example end-to-end. Daily habit: one theorem, one example, one exercise. Week 3: Bounded linear operators, spectral basics, compact