Báo cáo toán học: " Nonexistence of nontrivial solutions for the p(x)-Laplacian equations and systems in unbounded domains of Rn" docx

... akroutkamel@gmail.com; ∗ Corresponding author Abstract In this paper, we are interested on the study of the nonexistence of nontrivial solutions for the p (x) −Laplacian equations, in unbounded domains of R n . This ... versions will be made available soon. Nonexistence of nontrivial solutions for the p(x)-Laplacian equations and systems in...

Ngày tải lên: 20/06/2014, 21:20

... Gronwall inequality and similar energy method to the proof of Theorem 3.1 in Qin, Yang and Liu [10], we can deduce the boundedness of u and the existence of absorbing set. □ Lemma 4.2 Under the condition ... of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, People’s Republic of China Full list of author information is available at...

Ngày tải lên: 20/06/2014, 21:20

... (2.23) Using (2.23), (2.22), (2.1), (2.13), (1.1), (1.2), (1.6) and the H 2 -theory of the Stokes system, we arrive at u L ∞ (0,T ;H 2 ) ≤ C. This completes the proof.  Competing interests The ... L 1 (0, T ; ˙ B 0 ∞,∞ ) for the 3D Boussinesq system with partial viscosity. Later, in [3] Zhou and Fan studied the Cauchy problem of certain Boussinesq −α equations in...

Ngày tải lên: 20/06/2014, 21:20

... 0for u ∈ W\B r 2 (0 ) ,where B r 2 (0 ) is an open ball in W of radius r 2 centered at 0. Proof. The proof of Proposition 3.2 is the same as the proof of the condition (A2) in the proof of Theorem ... Fountain theorem, and the Symmetric Mountain Pass theorem. The rest of the article is divided as follows: Basic definitions and preliminary results are collect...

Ngày tải lên: 20/06/2014, 22:20

... that is originally not defined to use that information (e.g., the SNR information at the link layer or the queue size at the baseband module). The motivation for this special issue is the observation that ... knowledge. Acknowledgments The editors would like to thank all the reviewers for their efforts in making this special issue. They would also like to thank the Edito...

Ngày tải lên: 21/06/2014, 22:20

... to their desired BS benefit in the uplink. The reason for this opposite trend for the uplink and the downlink is elaborated in the following. Due to the specific point- to-multipoint structure in ... BB- ITS outperforms ASCA by a factor of 2.75 in terms of the lower 10%-ile of the downlink user throughput. On the other hand, the cell-edge user throughput...

Ngày tải lên: 21/06/2014, 23:20

... operators and domains, and the blowup questions for nonlinear parabolic equations and systems. We refer the interested reader to [20,22, 26, 27, 36–39], and some of the references therein. Our ... equivalence between integral and PDE systems for α = 2 can be verified as in the proof of Theorem 1 in [1]. For single equations, we refer to [2, The- orem 4....

Ngày tải lên: 20/06/2014, 21:20

... domains, and the blowup questions for nonlinear parabolic equations and systems. We refer the interested reader to [20,22, 26, 27, 36–39], and some of the references therein. Our results in the ... equivalence between integral and PDE systems for α = 2 can be verified as in the proof of Theorem 1 in [1]. For single equations, we refer to [2, The- orem...

Ngày tải lên: 20/06/2014, 21:20

... Thus, existing literature on the problem 1.1 is limited. In 1984, Agarwal and chow 1 firstly investigated the existence of the solutions of the problem 1.1 by contraction mapping and iterative ... solutions of the problem 1.2. In fact, there exist solutions w 1 , ,w k , such that for 1 ≤ j ≤ k, w j has exactly j − 1 simple zeros on the open interval 0...

Ngày tải lên: 21/06/2014, 16:20