The paper is devoted to the analysis of an abstract evolution inclusion with a non-invertible operator, motivated by problems arising in nonlocal phase separation modeling. Existence, uniqueness, and long-time behaviour of the solution to the related Cauchy problem are discussed in detail.
We investigate two boundary value problems for the second order differential equation with p-Laplacian (a(t)Φp(x ′ ))′ = b(t)F(x), t ∈ I = [0, ∞), where a, b are continuous positive functions on I. We give necessary and sufficient conditions which guarantee the existence of a unique (or at least one) positive solution, satisfying one of the following two boundary conditions: i) x(0) = c > 0, lim t→∞ x(t) = 0; ii) x ′ (0) = d < 0, lim t→∞ x(t) = 0.
This paper studies the uniqueness of meromorphic functions f n ∏ k i=1 (f (i) ) ni and g n ∏ k i=1 (g (i) ) ni that share two values, where n, nk, k ∈ N, ni ∈ N ∪ {0}, i = 1, 2, . . . , k − 1. The results significantly rectify, improve and generalize the results due to Cao and Zhang (2012).
With the aid of the notion of weighted sharing and pseudo sharing of sets we prove three uniqueness results on meromorphic functions sharing three sets, all of which will improve a result of Lin-Yi in Complex Var. Theory Appl. (2003).
The two-point boundary value problem u ′′ + h(x)u p = 0, a < x < b, u(a) = u(b) = 0 is considered, where p > 1, h ∈ C 1 [0, 1] and h(x) > 0 for a ≤ x ≤ b. The existence of positive solutions is well-known. Several sufficient conditions have been obtained for the uniqueness of positive solutions. On the other hand, a non-uniqueness example was given by Moore and Nehari in 1959. In this paper, new uniqueness results are presented.
We provide a simpler proof for a recent generalization of Nagumo's uniqueness theorem by A. Constantin: On Nagumo's theorem. Proc. Japan Acad., Ser. A 86 (2010), 41–44, for the differential equation $x'=f(t,x)$, $ x(0)=0$ and we show that not only is the solution unique but the Picard successive approximations converge to the unique solution. The proof is based on an approach that was developed in Z. S. Athanassov: Uniqueness and convergence of successive approximations for ordinary differential equations. Math. Jap. 35 (1990), 351–367. Some classical existence and uniqueness results for initial-value problems for ordinary differential equations are particular cases of our result.
Let k be a nonnegative integer or infinity. For a ∈ C ∪ {∞} we denote by Ek(a; f) the set of all a-points of f where an a-point of multiplicity m is counted m times if m ≤ k and k + 1 times if m > k. If Ek(a; f) = Ek(a; g) then we say that f and g share the value a with weight k. Using this idea of sharing values we study the uniqueness of meromorphic functions whose certain nonlinear differential polynomials share a nonzero polynomial with finite weight. The results of the paper improve and generalize the related results due to Xia and Xu (2011) and the results of Li and Yi (2011).
In this paper, we investigate the uniqueness problem of difference polynomials sharing a small function. With the notions of weakly weighted sharing and relaxed weighted sharing we prove the following: Let f(z) and g(z) be two transcendental entire functions of finite order, and α(z) a small function with respect to both f(z) and g(z). Suppose that c is a non-zero complex constant and n ≥ 7 (or n ≥ 10) is an integer. If f n (z)(f(z)−1)f(z +c) and g n (z)(g(z) − 1)g(z + c) share ''(α(z), 2)'' (or (α(z), 2)∗ ), then f(z) ≡ g(z). Our results extend and generalize some well known previous results.
Příspěvek je věnován pojetí vzácnosti, jedinečnosti a duševního vlastnictví.Autorův pohled je veden z hlediska platného českého práva, zejména nového občanského zákoníku z roku 2012. Téma je autorem
nahlíženo rámcem informační společnosti nebo společnosti sítí. Podstatná část textu je zaměřena na kritiku některých myšlenek právně informační filozofie, které směřují proti tradičnímu uznávání nehmotných majetkových hodnot na hospodářském trhu. Obsah textu spočívá též v kritickém srovnání sovětského systému, zejména vynálezeckého práva, s některými soudobými návrhy tzv. pirátských politických stran. and The paper is devoted to the concept of scarcity, uniqueness and the intellectual property. The author’s view is maintained in the terms of the recent Czech law, in particular the new Civil Code of 2012. The theme is analyzed with respect to information society or network society. A substantial
part of the text focuses on criticism of some ideas of the legal information philosophies directed against the traditional recognition of the intangible assets in the economic market. The content of the text is also dealing with a critical comparison of the former Soviet system, in particular the rights of the inventor, with some contemporary meanings of the so-called pirate political parties.
In this paper we study the uniqueness for meromorphic functions sharing one value, and obtain some results which improve and generalize the related results due to M. L. Fang, X. Y. Zhang, W. C. Lin, T. D. Zhang, W. R. Lü and others.