IMPULSIVE HIGHER-ORDER NONLINEAR AND FUNCTIONAL PROBLEMS

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.

Contents:

• Preface
• About the Authors
• Introduction
• Two-Point Impulsive Problems:
  • Higher-Order Nonlinear Impulsive Boundary Value Problems
  • Half-Linear Impulsive Third-Order Problem with General Jump Conditions
  • Semi-Linear Impulsive Higher-Order Boundary Value Problems
  • Periodic Third-Order Boundary Value Problems with Generalized Impulsive Conditions
  • Third-Order Generalized Discontinuous Impulsive Problems on the Half-Line
• Impulsive Coupled Systems:
  • First-Order Periodic Systems
  • Second-Order Impulsive Periodic Coupled Systems
  • Second-Order Coupled Impulsive Systems with Phi-Laplacian
  • Strongly Nonlinear Third-Order Impulsive Coupled Systems
  • Higher-Order Impulsive Systems with Phi-Laplacians
  • Functional Coupled Systems with Generalized Impulsive Conditions
• Bibliograph
• Index

Readership: Mathematicians, researchers, and academics in differential equations and nonlinear analysis. It is also suitable for engineering researchers in mathematical modeling of impulsive systems. The content targets graduate and PhD students in mathematics and engineering. Postdoctoral researchers working on impulsive differential equations and coupled nonlinear systems will also benefit.