This authoritative monograph presents in detail classical and modern methods for the study of semilinear elliptic equations, that is, methods to study the qualitative properties of solutions using variational techniques, the maximum principle, blowup analysis, spectral theory, topological methods, etc. The book is self-contained and is addressed to experienced and beginning researchers alike.

This book is to be a new edition of Applied Analysis. Several fundamental materials of applied and theoretical sciences are added, which are needed by the current society, as well as recent developments in pure and applied mathematics. New materials in the basic level are the mathematical modelling using ODEs in applied sciences, elements in Riemann geometry in accordance with tensor analysis used in continuum mechanics, combining engineering and modern mathematics, detailed description of optimization, and real analysis used in the recent study of PDEs. Those in the advance level are the...