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This monograph provides a complete and self-contained account of the theory, methods, and applications of constant-sign solutions of integral equations. In particular, the focus is on different systems of Volterra and Fredholm equations. The presentation is systematic and the material is broken down into several concise chapters. An introductory chapter covers the basic preliminaries. Throughout the book many examples are included to illustrate the theory. The book contains a wealth of results that are both deep and interesting.This unique book will be welcomed by mathematicians working on integral equations, spectral theory, and on applications of fixed point theory and boundary value problems.
List of contents
Introduction and Preliminaries.- System of Fredholm Integral Equations: Existence of a Constant-Sign Solution.- System of Fredholm Integral Equations: Eigenvalues.- System of Fredholm Integral Equations: Triple Constant-Sign Solutions.- System of Fredholm Integral Equations: Existence of a Constant-Sign Lp Solution.- System of Fredholm Integral Equations: Semipositone and Singular Case.- Systems of Fredholm and Volterra Integral Equations: Integrable Singularities.- Systems of Higher Order Boundary Value Problems: Integrable Singularities.- System of Volterra Integral Equations: Integrable Singularities.- Systems of Fredholm and Volterra Integral Equations: the Singular Case.- System of Singular Fredholm Integral Equations.- System of Singular Integral Equations of Hammerstein Type.- System Modeling the Spread of Interdependent Epidemics: Constant-Sign Periodic Solutions.- System of Hill's Equations: Constant-Sign Periodic Solutions.- System of Integral Equations: Constant-Sign Periodic and Almost Periodic Solutions.- System of Fredholm Integral Equations: Solutions in Orlicz Spaces.- System of Volterra Integral Equations: Constant-Sign Solutions in Orlicz Spaces.- System of Urysohn Integral Equations: Existence of a Constant-Sign Solution.- System of Fredholm Integral Equations: Existence Results via Brezis-Browder Arguments.- System of Volterra Integral Equations: Existence Results via Brezis-Browder Arguments.- Bibliography.- Subject Index.
Summary
This monograph provides a complete and self-contained account of the theory, methods, and applications of constant-sign solutions of integral equations. In particular, the focus is on different systems of Volterra and Fredholm equations. The presentation is systematic and the material is broken down into several concise chapters. An introductory chapter covers the basic preliminaries. Throughout the book many examples are included to illustrate the theory. The book contains a wealth of results that are both deep and interesting.
This unique book will be welcomed by mathematicians working on integral equations, spectral theory, and on applications of fixed point theory and boundary value problems.
Additional text
From the book reviews:
“The book is devoted to the study of nonlinear Volterra and Fredholm integral equations. This extremely clear, well-written and self-contained monograph offers to a wide class of readers a valuable theoretical foundation in the theory of nonlinear integral equations and their applications to nonlinear boundary value problems encountered in various fields of the physical, chemical, and biological sciences. … Throughout the book many mathematical examples are included to illustrate the theory.” (D. G. Natroshvili, Mathematical Reviews, June, 2014)
Report
From the book reviews:
"The book is devoted to the study of nonlinear Volterra and Fredholm integral equations. This extremely clear, well-written and self-contained monograph offers to a wide class of readers a valuable theoretical foundation in the theory of nonlinear integral equations and their applications to nonlinear boundary value problems encountered in various fields of the physical, chemical, and biological sciences. ... Throughout the book many mathematical examples are included to illustrate the theory." (D. G. Natroshvili, Mathematical Reviews, June, 2014)
