{"product_id":"linear-and-nonlinear-perturbations-of-the-operator-div","title":"Linear and Nonlinear Perturbations of the Operator Div","description":"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.","brand":"American Mathematical Society","offers":[{"title":"Default Title","offer_id":57186474295640,"sku":"9780821805862","price":174.84,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0278\/1295\/4195\/files\/9780821805862.jpg?v=1780110946","url":"https:\/\/agendabookshop.com\/products\/linear-and-nonlinear-perturbations-of-the-operator-div","provider":"Agenda Bookshop","version":"1.0","type":"link"}