Motreanu D. Nonlinear Differential Problems with Smooth and Nonsmooth Constraints

New York: Academic Press, 2018. — 355 p.Nonlinear Differential Problems with Smooth and Nonsmooth Constraints systematically evaluates how to solve boundary value problems with smooth and nonsmooth constraints. Primarily covering nonlinear elliptic eigenvalue problems and quasilinear elliptic problems using techniques amalgamated from a range of sophisticated nonlinear analysis domains, the work is suitable for PhD and other early career researchers seeking solutions to nonlinear differential equations. Although an advanced work, the book is self-contained, requiring only graduate-level knowledge of functional analysis and topology. Whenever suitable, open problems are stated and partial solutions proposed. The work is accompanied by end-of-chapter problems and carefully curated references.Prerequisites of functional analysis and operator theory
Prerequisites of regularity theory and maximum principle
Nonlinear elliptic eigenvalue problems
Nonlinear elliptic equations with general dependence on the solution gradient
Constant sign and sign-changing solutions for quasilinear elliptic problems
Nonlinear elliptic systems
Singular quasilinear elliptic systems
Evolutionary variational and quasivariational inequalities
Control problems for evolutionary differential inclusions