Georgiev S.G., Zennir K. Multiple Fixed-Point Theorems and Applications in the Theory of ODEs, FDEs and PDEs

CRC Press; Taylor & Francis Group, LLC, 2020 — 305 p. — (Monographs and Research Notes in Mathematics). — ISBN: 978-1-003-02872-7.Multiple Fixed-Point Theorems and Applications in the Theory of ODEs, FDEs and PDEs covers all the basics of the subject of fixed-point theory and its applications with a strong focus on examples, proofs and practical problems, thus making it ideal as course material but also as a reference for self-study.
Many problems in science lead to nonlinear equations T x + F x = x posed in some closed convex subset of a Banach space. In particular, ordinary, fractional, partial differential equations and integral equations can be formulated like these abstract equations. It is desirable to develop fixed-point theorems for such equations. In this book, the authors investigate the existence of multiple fixed points for some operators that are of the form T + F, where T is an expansive operator and F is a k-set contraction. This book offers the reader an overview of recent developments of multiple fixed-point theorems and their applications.Fixed-Point Index Theory. Multiple Fixed-Point Theorems
Applications to ODEs
Applications to FDEs
Applications to Parabolic Equations
Applications to Hyperbolic Equations
Applications to Elliptic Equations