Synopsis
This book focuses on advanced higher-order boundary value problems featuring instantaneous changes (impulses) in unknown functions and their derivatives. It explores novel applications of Laplacian operators, including p-Laplacian and Phi-Laplacian, specifically in discontinuous and impulsive settings — a topic rarely covered in current literature. The first part addresses nonlinear impulsive boundary value problems, using topological and analytical methods to tackle complex cases such as periodic solutions and unbounded domains. The second part delves into impulsive coupled systems, where multiple unknown functions interact and influence jump conditions, offering new insights into these understudied systems. Additionally, the book covers functional boundary conditions, generalizing traditional local boundary data to include integral, multi-point, and global constraints, expanding the scope of applications in mathematical modeling. Ideal for graduate and PhD students, postdoctoral researchers, and professionals in mathematics, engineering, mathematical biology, and applied sciences, this book provides rigorous mathematical tools and methods for solving challenging impulsive differential equations and nonlinear coupled systems.
About the Authors
Feliz Minhós is a PhD in Mathematics, Full Professor in the Department of Mathematics, University of Évora, Portugal, Coordinator of the Research Centre for Mathematics and Applications (CIMA), and former Director of the PhD Program in Mathematics and former Head of the Department of Mathematics of the University of Évora, reviewer of many international journals, Guest Editor of several Special Issues and member of the Editorial Board of various of international journals, Supervisor of several PhD theses concluded and ongoing, author or editor of various scientific and pedagogical books and more than hundred scientific papers in international journals, in multiple fields such as Mathematical Analysis, Differential Equations, Functional Analysis, among others.
Rui Carapinha is a PhD in Mathematics and Applications from the University of Évora, Portugal, with expertise in computational linguistics, software engineering, and high-performance data systems. His work focuses on the development of grammatical frameworks for integrating code generation languages under the Unified Modeling Language paradigm. At the European Organization for Nuclear Research (CERN) in Geneva, he contributed to the Large Hadron Collider (LHC) ATLAS experiment, designing and implementing database systems for storing and tracking subatomic particle data. His research and system design for the ATLAS Muon Spectrometer, Magnet System, Inner Detectors, and Calorimeters played a role in the 2012 discovery of the Higgs boson.
Gracino Rodrigues holds a Bachelor's degree in Mathematics from the Federal University of Alagoas, Brazil, a Professional Master's in Mathematics from PROFMAT — a national program coordinated by the Brazilian Mathematical Society (SBM) and supported by IMPA, and a PhD in Applied Mathematics from the University of Évora, Portugal. With extensive teaching experience, he serves as an educator in both Basic and Higher Education within Brazil's Federal Network, specializing in Applied Mathematics. He teaches courses in Civil Engineering, Electrical Engineering, and undergraduate programs in Chemistry, Physics, and Mathematics. His academic and professional expertise bridges theoretical and practical applications, fostering interdisciplinary learning.
Sara Perestrelo has both a BSc and an MSc in Physics specializing in Solid-state Physics from the University of Lisbon and is currently enrolled in a PhD in Mathematics at the University of Évora. Apart from her research, Sara has professional experience in high school level teaching in Mathematics and science outreach within the field of Astronomy and Astrophysics. The latter activity still holds in partnership with the Lake Alqueva Observatory. Most of her recent works were produced within the field of Analysis, on Existence and Localization of Periodic Solutions in ODEs, and Discrete Dynamical Systems, on Synchronization of Huygens Oscillators. Currently she is working as a risk analyst at Banco BPI, as a member of the Model Validation team.
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