Báo cáo hóa học: "Research Article Global Behavior of the Components for the Second Order m-Point Boundary Value Problems" potx

... (1.2)and(1.3). Then Theorem 2.3 implies the weak mean ergodic convergence of u(t, ·). In addition, if r(t) ≥−Mt −2 eventually, Corollary 2.5 implies the weak convergence of the solution to the above ... 1245–1252, 1982. [5] E. Mitidieri, “Some remarks on the asymptotic behaviour of the solutions of second order evolu- tion equations,” Journal of Mathematical Analysis...

Ngày tải lên: 22/06/2014, 18:20

... several lemmas before completing the proof of Theorem 1.4. By considering the restriction of the map T of 1.15 to m ∗ ,M ∗  2 , an application of the Schauder Fixed Point Theorem 17 gives ... converges to the equilibrium. Proof of Theorem 1.4. The four parts of the proof are as follows. a fx, y is increasing in both x and y on m ∗ ,M ∗  2 . By Lemma 5.2...

Ngày tải lên: 21/06/2014, 20:20

... Corporation Boundary Value Problems Volume 2008, Article ID 254593, 10 pages doi:10.1155/2008/254593 Research Article Global Behavior of the Components for the Second Order m-Point Boundary Value Problems Yulian ... the global behavior of the components of nodal solutions of 1.8, 1.9 and give a positive answer to the above question. Howeve...

Ngày tải lên: 22/06/2014, 06:20

... condition for the local stability of the difference equation x nk  s 1 x nk−1  ··· s k x n  0,n 0, 1, 2.4 3. The Main Results and Their Proofs In this section, we investigate the globally ... conditions x −m ,x −m1 , ,x 1 ,x 0  ∈ 0,μ m1 . Proof. The proof of this Theorem is similar to that of Theorem 3.3. We omit the details. Theorem 3.6. If 0 <D<1,  l...

Ngày tải lên: 21/06/2014, 11:20

... Corporation Boundary Value Problems Volume 2011, Article ID 715836, 12 pages doi:10.1155/2011/715836 Research Article Global Structure of Nodal Solutions for Second- Order m-Point Boundary Value Problems with ... of the components f or the second order m-point boundary value problems,” Boundary Value Problems, vol. 2008, Article ID 254593, 10 pag...

Ngày tải lên: 21/06/2014, 11:20

... is the monotonicity of the half-eigenvalues on the weights a, b. The other is the infimum H F m,γ r can be attained by some weights for any γ ∈ 1, ∞.As consequence of these two facts, for ... boundary conditions see 7–10. As an elementary application of such a stronger continuity, the proof of the first step, that is, the existence of minimizers or maxi...

Ngày tải lên: 21/06/2014, 11:20

... cross-diffusive models, at least for small values of the cross diffusivities. Consequently, all the available information for linear diffusive models is essential to realize the behavior of the most complicated ... α 31  α 32  0, then 1.1 reduces to the system 1.4 of Part I. Recently, the work in 18–20 studied the existence, uniform boundedness, and uniform conv...

Ngày tải lên: 21/06/2014, 20:20

... ≤ G  u  T   P. 2.53 The rest of the proof is similar to that of Theorem 2.8, and the details are omitted. The proof is completed. Theorem 2.10. Assume that the function ft, u 0 , ,u n−1  ... equations. Many other interesting time scales exist, and they give rise to many applications see 2. Not only the new theory of the so-called “dynamic equations” unifies th...

Ngày tải lên: 21/06/2014, 05:20

... estimates are crucial for the proof of the existence of the maximal periodic solution and the asymptotic boundedness of the nonnegative solutions of the initial boundary value problem. This paper ... properties of the weak solutions of the initial boundary value problem see 17–22 and references therein. Maddalena 20 especially, established the exi...

Ngày tải lên: 21/06/2014, 07:20

... and A 2 . In the following, we give the attractivity of the zero solution and the proof is similar to that of Theorem 3.3. Corollary 3.5. If A 1 −A 4  hold with I  0, then the zero solution of 2.4 ... 0inTheorem 3.3. It follows from Theorem 3.3 that the set S is also a global attracting set of 2.4. The proof is complete. For the case I  0, we easily obs...

Ngày tải lên: 21/06/2014, 20:20