Báo cáo hóa học: " Research Article The Best Constant of Sobolev Inequality Corresponding to Clamped Boundary Value Problem" pdf

... Corporation Boundary Value Problems Volume 2011, Article ID 875057, 17 pages doi:10.1155/2011/875057 Research Article The Best Constant of Sobolev Inequality Corresponding to Clamped Boundary Value ... s. Clearly, Theorem 1.2i, ii is rewritten equivalently as follows. Corollary 1.3. Let u ∈ H, then the best constant of Sobolev inequality (corre...

Ngày tải lên: 21/06/2014, 05:20

... provided the original work is properly cited. We give the best lower bound for the weighted Jensen’s discrete inequality with ordered variables applied to a convex function f, in the case when the ... Variables Vasile Cirtoaje Department of Automatic Control and Computers, University of Ploiesti, 100680 Ploiesti, Romania Correspondence should be addressed to Vasile Cirto...

Ngày tải lên: 21/06/2014, 07:20

... operator A : −2, ∞ → −2, ∞ doesn’t satisfy the definition of u 0 -concave operators. Therefore, we can’t obtain the fixed point of A by the fixed point theorem of u 0 -concave operators. The ... generalize the concept of u 0 -concave operators, give a concept of the generalized u 0 -concave operators, and study the existence and uniqueness of fixed points for this...

Ngày tải lên: 21/06/2014, 07:20

... 1 −nn −k k r −r Figure 4: The example of the position of the referent and assigned element of the nested HS function in the block-matrix in the space of the selected hyperspheric block-matrix. According to the translator ... and therefore we develop specific translators of the ϑΔk, Δn, 0 type. On the basis of the established graph, all option relations ar...

Ngày tải lên: 21/06/2014, 11:20

... nontrivial solution of the BVP 1.1 and 1.2. Next, we show the uniqueness of solutions of the BVP 1.1 and 1.2. Assume, to the contrary, that there exist two nontrivial solutions y 1 and y 2 of the BVP ... the proof of the theorem. Remark 3.2. From the proof of Theorem 3.1, we easily know that assume y  Ay,x, x  A x, y,thus,lety 0  y, x 0  x, we hav...

Ngày tải lên: 21/06/2014, 18:20

... t 0 . 2.11 4 Boundary Value Problems In view of 1.11 and the definition of G n t, s, we can obtain ut ≥ 0,t∈ 0,b n . This completes the proof of Lemma 1.3. Now we state the main results of this ... Introduction and the Main Results In this paper, we will consider the existence and uniqueness of positive solutions to a class of second-order singular m-point...

Ngày tải lên: 21/06/2014, 20:20

... that resembles the sawtooth waveform. With P<.5, the maximum of the waveform is closer to the beginning of oscillation period, and when P>.5, the maximum is closer to the end of the period. ... antialiasing oscillator algorithms roll off faster than that of the textbook sawtooth, which means that their spectra are already closer to the spectrum of the...

Ngày tải lên: 21/06/2014, 05:20

... 0witha /  b. For more results, see 9–23. The purpose of the present paper is to find the greatest values α 1 ,α 2 and the least values β 1 ,β 2 such that the double inequalities α 1 C  a, b    1 ... ∞. Acknowledgments The authors wish to thank the anonymous referees for their very careful reading of the paper and fruitful comments and suggestions. This researc...

Ngày tải lên: 21/06/2014, 05:20

... ≤x≤R. The proof is complete. 5. Discussion In this section, we offer some interesting discussion associated with boundary value problems 1.5. Since the proof of the main theorem Theorem 4.1 ... 1, s ∈ 0, 1. Proof. From the properties of G 1 t, s, and the definition of G 2 t, s, we can prove that the results of Proposition 2.3 hold. Theorem 2.4. If μ ∈ 0,α−...

Ngày tải lên: 21/06/2014, 05:20

... common element of the set of fixed points of strictly pseudocontractive mappings, the set of common solutions of generalized mixed equilibrium problems, and the set of common solutions of the variational ... common element of the set of fixed point of strictly pseudocontractive mappings, the set of common solutions of variational inequalities with inverse-str...

Ngày tải lên: 21/06/2014, 05:20