by Junping Shi (College of William & Mary, USA)

This volume provides a unified approach to the problem of exact multiplicity and global bifurcation of semilinear elliptic equations, demonstrating applications of modern bifurcation theory to important nonlinear equations in physics, chemistry and biology. In particular, it lucidly presents a systematic theory of precise bifurcation diagrams for the development of radially symmetric solutions over the last thirty years.

The volume is an essential reference for researchers in the fields of nonlinear elliptic and parabolic equations, as well as many applied fields in physics, chemistry and biology. Self-contained and assuming only a basic knowledge of analysis and differential equations, it may also be used as an advanced textbook by graduate students in mathematics and nonlinear sciences.

• Bifurcation Theory for PDE
• Imperfect Bifurcation
• Solution Set and Global Bifurcation Diagrams for General Bounded Domains
• Exact Multiplicity and Global Bifurcation Diagrams for Spherical Domains
• Properties of Solutions in Whole Space and Half Space
• Solution Set for Symmetric Domains
• Singularly Perturbed Problems