Translations of Mathematical Monographs 1994; 348 pp; hardcover Volume: 139 ISBN10: 0821846167 ISBN13: 9780821846162 List Price: US$129 Member Price: US$103.20 Order Code: MMONO/139
 The theory of nonlinear elliptic equations is currently one of the most actively developing branches of the theory of partial differential equations. This book investigates boundary value problems for nonlinear elliptic equations of arbitrary order. In addition to monotone operator methods, a broad range of applications of topological methods to nonlinear differential equations is presented: solvability, estimation of the number of solutions, and the branching of solutions of nonlinear equations. Skrypnik establishes, by various procedures, a priori estimates and the regularity of solutions of nonlinear elliptic equations of arbitrary order. Also covered are methods of homogenization of nonlinear elliptic problems in perforated domains. The book is suitable for use in graduate courses in differential equations and nonlinear functional analysis. Readership Researchers, mathematicians, and graduate students studying differential equations and nonlinear functional analysis. Reviews "This is a nice and useful book representing a systematic approach to nonlinear elliptic partial differential equations with several interesting examples and applications."  Zentralblatt MATH Table of Contents  Mappings of monotone type and solvability of quasilinear boundary value problems
 Degree of generalized monotone mappings
 Topological characteristics of nonlinear elliptic boundary value problems
 Solvability and behavior of solutions of nonlinear elliptic boundary value problems
 Solvability of the nonlinear Dirichlet problem in a narrow strip
 Solvability of semilinear boundary value problems
 A priori estimates and regularity of solutions of higher order quasilinear elliptic equations
 Behavior of solutions of quasilinear elliptic equations near the boundary
 Nonlinear elliptic problems in domains with finegrained boundary
 Homogenization of nonlinear Dirichlet problems in domains with channels
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