Matches in SemOpenAlex for { <https://semopenalex.org/work/W216427907> ?p ?o ?g. }
Showing items 1 to 80 of
80
with 100 items per page.
- W216427907 abstract "As described in Section 24 it is our intention to develop a smoothness theory for some semi-linear integral equations and differential equations with prototypes (24.6), (24.7). It is natural to interpret the right-hand side of (24.6) as an operator and to ask for a fixed point in a suitable (real) function space. As a minimal requirement, the operators T and T+, given by (25.4) and (25.5), should be bounded in such function spaces. By Theorem 25.8 we have a rather satisfactory answer. Let, for example, ( h in mathbb{B}_{pq}^sleft( {{mathbb{R}^n}} right)) in (24.6) with ( left( {frac{1}{p},s} right) in {R_n}) according to (25.40). Then it is natural to ask for solutions ( u in mathbb{B}_{pq}^sleft[ {{mathbb{R}^n}} right]) with (24.6). However at least at first glance there are no fixed point theorems which can be applied. Since we are in ℝ n there is no compactness such that Schauder or Leray-Schauder arguments can be used. Banach’s fixed point theorem (contraction mappings) in ( mathbb{B}_{pq}^sleft( {{mathbb{R}^n}} right)) does not work if ( left( {frac{1}{p},s} right) in {R_n}) as above, since by Theorem 25.14 the operatorsT+andThave poor continuity properties. This is the point where the Q-operator, roughly described so far in (24.8), (24.9), comes in. It has much better properties thanTandT+.Under some posi-tivity assumptions for the kernelsKit produces supersolutions of (24.6) and its generalizations. Together with the supersolution technique which will be described in 27 one gets finally solutions of (24.6), and also of (24.7),with optimal smoothness properties.In the present we study the operatorQ.Based on quarkonial decompositions as proved in 2 one obtains rather easily the described assertions." @default.
- W216427907 created "2016-06-24" @default.
- W216427907 creator A5064194525 @default.
- W216427907 date "2001-01-01" @default.
- W216427907 modified "2023-09-26" @default.
- W216427907 title "The Q-operator" @default.
- W216427907 doi "https://doi.org/10.1007/978-3-0348-8257-6_26" @default.
- W216427907 hasPublicationYear "2001" @default.
- W216427907 type Work @default.
- W216427907 sameAs 216427907 @default.
- W216427907 citedByCount "0" @default.
- W216427907 crossrefType "book-chapter" @default.
- W216427907 hasAuthorship W216427907A5064194525 @default.
- W216427907 hasConcept C104317684 @default.
- W216427907 hasConcept C112698675 @default.
- W216427907 hasConcept C114614502 @default.
- W216427907 hasConcept C118615104 @default.
- W216427907 hasConcept C132954091 @default.
- W216427907 hasConcept C134306372 @default.
- W216427907 hasConcept C144133560 @default.
- W216427907 hasConcept C146147875 @default.
- W216427907 hasConcept C158448853 @default.
- W216427907 hasConcept C17020691 @default.
- W216427907 hasConcept C185592680 @default.
- W216427907 hasConcept C18648836 @default.
- W216427907 hasConcept C202444582 @default.
- W216427907 hasConcept C2780129039 @default.
- W216427907 hasConcept C28642324 @default.
- W216427907 hasConcept C33923547 @default.
- W216427907 hasConcept C34388435 @default.
- W216427907 hasConcept C45962547 @default.
- W216427907 hasConcept C55493867 @default.
- W216427907 hasConcept C86339819 @default.
- W216427907 hasConceptScore W216427907C104317684 @default.
- W216427907 hasConceptScore W216427907C112698675 @default.
- W216427907 hasConceptScore W216427907C114614502 @default.
- W216427907 hasConceptScore W216427907C118615104 @default.
- W216427907 hasConceptScore W216427907C132954091 @default.
- W216427907 hasConceptScore W216427907C134306372 @default.
- W216427907 hasConceptScore W216427907C144133560 @default.
- W216427907 hasConceptScore W216427907C146147875 @default.
- W216427907 hasConceptScore W216427907C158448853 @default.
- W216427907 hasConceptScore W216427907C17020691 @default.
- W216427907 hasConceptScore W216427907C185592680 @default.
- W216427907 hasConceptScore W216427907C18648836 @default.
- W216427907 hasConceptScore W216427907C202444582 @default.
- W216427907 hasConceptScore W216427907C2780129039 @default.
- W216427907 hasConceptScore W216427907C28642324 @default.
- W216427907 hasConceptScore W216427907C33923547 @default.
- W216427907 hasConceptScore W216427907C34388435 @default.
- W216427907 hasConceptScore W216427907C45962547 @default.
- W216427907 hasConceptScore W216427907C55493867 @default.
- W216427907 hasConceptScore W216427907C86339819 @default.
- W216427907 hasLocation W2164279071 @default.
- W216427907 hasOpenAccess W216427907 @default.
- W216427907 hasPrimaryLocation W2164279071 @default.
- W216427907 hasRelatedWork W1004196404 @default.
- W216427907 hasRelatedWork W1991818427 @default.
- W216427907 hasRelatedWork W2003229492 @default.
- W216427907 hasRelatedWork W2048243301 @default.
- W216427907 hasRelatedWork W2092413778 @default.
- W216427907 hasRelatedWork W2144455792 @default.
- W216427907 hasRelatedWork W2196799668 @default.
- W216427907 hasRelatedWork W2314013901 @default.
- W216427907 hasRelatedWork W2319534107 @default.
- W216427907 hasRelatedWork W2322006997 @default.
- W216427907 hasRelatedWork W2380421720 @default.
- W216427907 hasRelatedWork W2393506115 @default.
- W216427907 hasRelatedWork W2490087123 @default.
- W216427907 hasRelatedWork W257415149 @default.
- W216427907 hasRelatedWork W2750597935 @default.
- W216427907 hasRelatedWork W2804215844 @default.
- W216427907 hasRelatedWork W2809375726 @default.
- W216427907 hasRelatedWork W3156162735 @default.
- W216427907 hasRelatedWork W3164742807 @default.
- W216427907 hasRelatedWork W89015498 @default.
- W216427907 isParatext "false" @default.
- W216427907 isRetracted "false" @default.
- W216427907 magId "216427907" @default.
- W216427907 workType "book-chapter" @default.