Focusing on nonlinear partial differential equations, this monograph presents advanced results and techniques centered around critical points. It compiles a variety of proofs, including the author's original contributions, ensuring a rigorous approach throughout. The book serves as a vital resource for researchers interested in recent advancements in this dynamic field and highlights the diverse applications of critical point theory.
Focusing on the general linear partial differential equation of arbitrary order m, this book explores the complexity and diversity of methods required to solve these equations, highlighting that only a small percentage have been successfully addressed. It delves into the conditions under which these equations can be solved and the number of possible solutions, emphasizing the intricate nature of partial differential equations across various scientific disciplines.