Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations
Contemporary Mathematics and Its Applications
Volume 6						

Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations

Vicentţiu D. Rădulescu

This text is concerned with the qualitative aspects of the theory of nonlinear elliptic partial differential equations, equations which can be seen as nonlinear variations of the classical Laplace equation. They appear as mathematical models in different branches of physics, chemistry, biology, genetics, and engineering and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on variation calculus and functional analysis.

Concentrating on single-valued or multivalued elliptic equations with nonlinearities of various types, the aim of this volume is to obtain sharp existence or nonexistence results, as well as decay rates for general classes of solutions. The estimates we obtain are the building blocks in understanding the qualitative theory, while the decay rates pave the way to the fine study of asymptotic. Many technically relevant questions are presented and analyzed in detail. A systematic picture of the most relevant phenomena is obtained for the equations under study, including bifurcation, stability, asymptotic analysis, and optimal regularity of solutions.

The method of presentation should appeal to readers with different backgrounds in functional analysis and nonlinear partial differential equations. All chapters include detailed heuristic arguments providing thorough motivation of the study developed later on in the text, in relationship with concrete processes arising in applied sciences. The book includes an extensive bibliography and a rich index, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of nonlinear phenomena described by elliptic partial differential equations.

This book provides a comprehensive and systematic guide to nonlinear partial differential equations of elliptic type.

End-of-chapter notes provide bibliographical comments and historical remarks.

Readership: Graduates and researchers in mathematics, physical sciences, and engineering.