Translations of Mathematical Monographs 1997; 104 pp; hardcover Volume: 160 ISBN10: 082180586X ISBN13: 9780821805862 List Price: US$62 Member Price: US$49.60 Order Code: MMONO/160
 The perturbation theory for the operator div is of particular interest in the study of boundaryvalue problems for the general nonlinear equation \(F(\dot y,y,x)=0\). Taking as linearization the first order operator \(Lu=C_{ij}u_{x_j}^i+C_iu^i\), one can, under certain conditions, regard the operator \(L\) as a compact perturbation of the operator div. This book presents results on boundaryvalue problems for \(L\) and the theory of nonlinear perturbations of \(L\). Specifically, necessary and sufficient solvability conditions in explicit form are found for various boundaryvalue problems for the operator \(L\). An analog of the Weyl decomposition is proved. The book also contains a local description of the set of all solutions (located in a small neighborhood of a known solution) to the boundaryvalue problems for the nonlinear equation \(F(\dot y, y, x) = 0\) for which \(L\) is a linearization. A classification of sets of all solutions to various boundaryvalue problems for the nonlinear equation \(F(\dot y, y, x) = 0\) is given. The results are illustrated by various applications in geometry, the calculus of variations, physics, and continuum mechanics. Readership Graduate students and research mathematicians interested in partial differential equations. Table of Contents  Notation
 Linear perturbations of the operator div
 Nonlinear perturbations of the operator div
 Appendix
 References
