{"product_id":"viability-invariance-and-applications-volume-207-9780444527615","title":"Viability, Invariance and Applications: Volume 207","description":"\u003cp\u003e • Author(s): Ovidiu Carja | Mihai Necula | Ioan I. Vrabie\u003cbr\u003e • Publisher: Elsevier Science\u003cbr\u003e • Publisher Imprint: Elsevier Science\u003cbr\u003e • BISAC: Differential Equations - Ordinary\u003c\/p\u003e\u003cp\u003eThe book is an almost self-contained presentation of the most important concepts and results in viability and invariance. The viability of a set K with respect to a given function (or multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. The invariance of a set K with respect to a function (or multi-function) F, defined on a larger set D, is that property which says that each solution of the differential equation (or inclusion) driven by F and issuing in K remains in K, at least for a short time.The book includes the most important necessary and sufficient conditions for viability starting with Nagumo's Viability Theorem for ordinary differential equations with continuous right-hand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In the latter (i.e. multi-valued) cases, the results (based on two completely new tangency concepts), all due to the authors, are original and extend significantly, in several directions, their well-known classical counterparts.\u003c\/p\u003e","brand":"Elsevier Science","offers":[{"title":"Hardcover","offer_id":47585975992471,"sku":"9780444527615","price":12174.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780444527615.webp?v=1774962264","url":"https:\/\/atlanticbooks.com\/products\/viability-invariance-and-applications-volume-207-9780444527615","provider":"Atlantic Books","version":"1.0","type":"link"}