Linear and Nonlinear Perturbations of the Operator Div is popular PDF and ePub book, written by Viktor Grigorʹevich Osmolovskiĭ in 1997, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Linear and Nonlinear Perturbations of the Operator Div can be Read Online from any device for your convenience.
Linear and Nonlinear Perturbations of the Operator Div Book PDF Summary
The perturbation theory for the operator div is of particular interest in the study of boundary-value 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 boundary-value problems for $L$ and the theory of nonlinear perturbations of $L$. Specifically, necessary and sufficient solvability conditions in explicit form are found for various boundary-value 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 boundary-value 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 boundary-value 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.
Detail Book of Linear and Nonlinear Perturbations of the Operator Div PDF
- Author : Viktor Grigorʹevich Osmolovskiĭ
- Release : 21 September 1997
- Publisher : American Mathematical Soc.
- ISBN : 082180586X
- Genre : Mathematics
- Total Page : 104 pages
- Language : English
- PDF File Size : 16,8 Mb
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