BOUNDARY VALUE PROBLEMS FOR ANALYTIC FUNCTIONS IN THE CLASS OF CAUCHY-TYPE INTEGRALS WITH DENSITY IN pot

... G(t)Φ − (t)+g(t), for analytic functions in the class of analytic functions represented by the Cauchy-type integrals with density in the spaces L p(·) (Γ) with variable exponent. We consider both the case ... solution of (1.1) in the class of analytic functions represented by the Cauchy-type integral with density in the spaces L p(...

Ngày tải lên: 23/06/2014, 00:20

... (2.12) Proof (see [3, Lemma 2.3]). The gauge transform is the Coulomb one given in the Lemma 2.1.  Considering the gauge invariance of the ᏿ᐃ α -theory, and the fact that the gauge group Ᏻ α is an in nite-dimensional ... studied in [3] and the topological ones in [1]. Thus, the main aim here is to obtain the existence of a solution to t he nonhomogeneous equati...

Ngày tải lên: 23/06/2014, 00:20

... ,∞ ,in 4.18 can be determined. The procedure describing the method of their deriving is a crucial part of the proof of Theorem 4.1 where we give their form as well. Proof. Substitute 4.18 into ... the existence of solutions in a relevant space and, moreover, to the construction of a family of linearly independent solutions of such problems in a general case w...

Ngày tải lên: 21/06/2014, 16:20

... below). For information about publishing your research in Advances in Difference Equations go to http://www.advancesindifferenceequations.com/authors/instructions/ For information about other SpringerOpen ... 16e 3−4e 2 (1−e) < 0. Therefore, together with Theorem 3.3, it follows that the problem (4.2) has at least two positive solutions. Competing interests The authors have n...

Ngày tải lên: 21/06/2014, 17:20

... are interesting aspects of the positive solutions for two kinds of m-point boundary value problems for an increasing homeomorphism and positive homo- morphism on time scales. By using the Avery–Peterson ... Avery–Peterson fixed point theorem, we obtain the existence of at least three positive solutions for these problems. The interesting point is that the nonlinear...

Ngày tải lên: 21/06/2014, 17:20

... recently, by using Shauder fixed point theorem, Guo 15 obtained the existence of positive solutions for a class of nth-order nonlinear impulsive singular integro-differential equations in a Banach ... H 1  and the absolute continuity of Lebesgue integral that {A  1 V t} is equicontinuous on any finite subinterval of J. In the following, we are in position to show t...

Ngày tải lên: 21/06/2014, 20:20

... 2.9 Advances in Difference Equations 3 In Section 2 we present some preliminary ideas that will be used in the remainder of the paper. In Section 3 we give sufficient conditions for the existence of at ... By the Contraction Mapping Principal, there exists a unique solution of 3.1 and the proof is complete. 2 Advances in Difference Equations In 12, the author...

Ngày tải lên: 21/06/2014, 20:20

... Introduction With the development of boundary value problems for differential equations [1–5], dif- ference equations [6, 7], and the theory of time scales [8–12], the existence of solutions for boundary value ... are interesting aspects of the positive solutions for two kinds of m-point boundary value problems for an increasing homeomorphism and pos...

Ngày tải lên: 21/06/2014, 20:20

... 3.14 The Leray-Schauder principle guarantees a fixed point of K, which is easily seen to be a solution of E3.2. By using a similar method to Theorem 3.2, one can deduce the following result. Theorem ... a solution. For the uniqueness, if u·,v· are two solutions of E2.2,setwt ut − vt, then w  tAwt,andwt−wt  T,fort ∈ R. Following the obvious Boundary...

Ngày tải lên: 21/06/2014, 20:20

... Domoshnitsky, “Maximum principles and boundary value problems, mathematical models in engineering, biology and medicine,” in Proceedings of the International Conference on Boundary Value Problems, A. Cabada, ... estimates of the spectral radii of the operators in the spaces of discontinuous functions, for example, in the spaces of summable or essential...

Ngày tải lên: 22/06/2014, 03:20