[PDF] Top 20 Maximal regular boundary value problems in Banach valued function spaces and applications

... the maximal regularity of parabolic nonlocal initial bound- ary value problems is ...In applications, the nonlocal boundary value problems for quasi elliptic partial di ff ... See full document

... Boundary value problems (BVPs) for differential-operator equations (DOEs) in abstract spaces have been studied extensively by many researchers ...The maximal regularity properties for ... See full document

... Correspondingly, applications of the theory of impulsive differential equations to different areas were considered by many authors, and some basic results on impulsive differential equations have been obtained; see ... See full document

... The theory of impulsive differential equations has become an important area of investigation in recent years, stimulated by their numerous applications to problems from mechanics, electrical engineering, ... See full document

... these spaces, including boundedness for H ∞ functions of A and ‘regularity shifting’ estimates for operators such as powers of A, are collected in Subsection ... See full document

... initial value problems, such as the dynamics of populations subject to abrupt changes (harvest- ing, diseases, ...and applications of impulsive differential ...initial value problems of ... See full document

... world problems. For more details about fractional calculus and its applications we refer the reader to the monographs of Hilfer [6], Kilbas et ...in Banach spaces were studied by Balachandran ... See full document

... Boundary value problems with integral boundary conditions constitute a very interesting and important class of ...nonlocal boundary value problems as special cases. ... See full document

... the maximal regularity properties for undegenerate DOEs were investigated, ...]. Regular degenerate DOEs in Banach spaces were treated in [–, , –, ...of Banach ... See full document

... ordered Banach space X for a Fr´ echet differentiable mapping T : X → X ...the applications of their results in ODE initial value problems and semilinear parabolic initial boundary ... See full document

... in Banach-valued Besov spaces have been studied in [4, 5, 27, ...of boundary value problems for elliptic differential-operator equations (DOE’s) have been refined in [3–7, 13, ... See full document

... the maximal regularity, Fredholmness, qualitative properties of the resolvent, and the completeness of the root elements of differential operators that are generated by these boundary value ... See full document

... Moreover, boundary value problems for di ff erential-operator equations have been stud- ied in detail by [16, 27, 30, ...of boundary value prob- lems for elliptic differential-operator ... See full document

... space valued function spaces have been studied extensively in the literature see 1–14 and the references ...therein. Maximal regularity properties for higher-order degenerate anisotropic DOEs ... See full document

... the Cartesian product of two cones in the space PC[0, 1], and using the well-known fixed point theorem of cone expansion and compression, we obtain conditions for the existence and multiplicity of positive solutions of ... See full document

... The structure of this paper is as follows. In Section  and Section , we introduce the Leggett-Williams fixed point theorem, some definitions, and some lemmas. In particular, we deduce system () and some properties of ... See full document

... integral boundary value problems of ordinary differential equations arise in dif- ferent areas of applied mathematics and physics such as heat conduction, underground water flow, thermo-elasticity and ... See full document

... impulsive problems for fractional differential equations with boundary value ...the boundary value problems for impulsive fractional differential ...integral boundary ... See full document

... For a bounded set V in a Banach space, we denote by α(V) the Kuratowski measure of noncompactness (see [–] for further understanding). In this paper, we denote by α(·) the Kuratowski measure of noncompactness of ... See full document

... Definition . Let E be an ordered Banach space, D be a bounded set of E. The opera- tor A : D → E is said to be a k-set contraction if A : D → E is continuous and bounded, and there is a constant k ≥  such that ... See full document