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This self-contained textbook provides the basic, abstract tools used in nonlinear analysis and their applications to semilinear elliptic boundary value problems. By first outlining the advantages and disadvantages of each method, this comprehensive text displays how various approaches can easily be applied to a range of model cases. An Introduction to Nonlinear Functional Analysis and Elliptic Problems is divided into two parts: the first discusses key results such as the Banach contraction principle, a fixed point theorem for increasing operators, local and global inversion theory, Leray–Schauder degree, critical point theory, and bifurcation theory; the second part shows how these abstract results apply to Dirichlet elliptic boundary value problems.  The exposition is driven by numerous prototype problems and exposes a variety of approaches to solving them. Complete with a preliminary chapter, an appendix that includes further results on weak derivatives, and chapter-by-chapter exercises, this book is a practical text for an introductory course or seminar on nonlinear functional analysis.

Functional analysis. --- Nonlinear functional analysis. --- Differential equations, Elliptic --- Nonlinear functional analysis --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Functional calculus --- Mathematics. --- Dynamics. --- Ergodic theory. --- Partial differential equations. --- Functional Analysis. --- Partial Differential Equations. --- Dynamical Systems and Ergodic Theory. --- Calculus of variations --- Functional equations --- Integral equations --- Functional analysis --- Nonlinear theories --- Differential equations, partial. --- Differentiable dynamical systems. --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Partial differential equations --- Differential equations, Elliptic. --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics

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L’ironie et l’humour, ces frères ennemis si familiers mais si insaisissables, sont depuis trop longtemps associés à des clichés consacrés par la littérature et par la critique littéraire. Afin de dépasser la taxinomie et le confort intellectuel des étiquettes, il est nécessaire de délier les deux notions de leur immédiateté référentielle ainsi que de leurs implications morales. Partant de l’intuition qu’il existe entre elles une dynamique esthétique, le présent ouvrage analyse leur fonctionnement stylistique. Il étudie la question des relations esthétiques entre l’ironie et l’humour en les envisageant à partir du regard du créateur sur l’œuvre d’art et sur le langage comme manifestation de sa subjectivité - et en considérant le rôle actif du lecteur. Esta obra aborda de manera conjunta las nociones de ironía y de humor en el ámbito de la cultura española, considerándolas a partir de la mirada del creador sobre la obra de arte y sobre el lenguaje. La mayoría de los trabajos desarrollados hasta ahora han privilegiado sus implicaciones satíricas, moralizadoras e ideológicas. El objetivo aquí es tratar de superar las clasificaciones tradicionales de estos dos conceptos, tan familiares como inasibles.

Irony in literature. --- Humor in literature. --- Spanish literature --- History and criticism.