This book deals with nonlinear boundary value problems for semilinear elliptic equations on unbounded domains with nonlinearities involving the subcritical Sobolev exponent. The variational problems investigated in the book originate in many branches of applied science. A typical example is the nonlinear Schrödinger equation which appears in mathematical modeling phenomena arising in nonlinear optics and plasma physics. Solutions to these problems are found as critical points of variational functionals. The main difficulty in examining the compactness of Palais-Smale sequences arises from the fact that the Sobolev compact embedding theorems are no longer true on unbounded domains. In this book we develop the concentration-compactness principle at infinity, which is used to obtain the relative compactness of minimizing sequences. This tool, combined with some basic methods from the Lusternik-Schnirelman theory of critical points, is to investigate the existence of positive, symmetric and nodal solutions. The book also emphasizes the effect of the graph topology of coefficients on the existence of multiple solutions.

Semilinear elliptic equations play an important role in many areas of mathematics and its applications to other sciences. This book presents a wealth of modern methods to solve such equations. Readers of this exposition will be advanced students and researchers in mathematics, physics and other.

Designed for all who provide emergency care, CEDT provides ready information needed to both diagnose and treat life-threatening conditions rapidly. This edition includes new or expanded material on heart emergencies, pediatric emergencies, and disaster management.

Established as an essential resource for medical students preparing for clinical rotations and the USMLE, Boards and Wards for USMLE Steps 2 & 3 is now in its updated Fifth Edition! Written in a succinct, high-yield outline format, it provides broad coverage of all key medical subspecialties in a user-friendly and portable format.