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.