Báo cáo hóa học: "Research Article Global Behavior of the Components for the Second Order m-Point Boundary Value Problems" potx
Báo cáo hóa học: " Research Article Asymptotic Behavior of Solutions to Some Homogeneous Second-Order Evolution Equations of Monotone Type" potx
... (1.2)and(1.3). Then Theorem 2.3implies the weak mean ergodic convergence of u(t,·). In addition, if r(t) ≥−Mt−2eventually, 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 and Applications, vol. 107, ... to Theorem 2.4, we have the following weak convergence theorem.Theorem 2.5. Suppose that the assumptions in Theorems 2.3 and 2.4 are satisfied. Thenu(t) p∈ A−1(0) as t → +∞.In our next theorem,...
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Báo cáo hóa học: " Research Article Global Behavior of Solutions to Two Classes of Second-Order Rational Difference Equations Sukanya Basu and Orlando Meri" docx
... 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 fx, y is increasing in both x and y on m∗,M∗2. By Lemma 5.2 the hypotheses of Theorem ... m∗,M∗2. The proof of Theorem 1.4 may be reproduced here in its entirety with the only change being the elimination of the case r<0, which presently does not apply. Everything else in the proofapplies...
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Báo cáo hóa học: "Research Article Global Behavior of the Components for the Second Order m-Point Boundary Value Problems" potx
... Corporation Boundary Value ProblemsVolume 2008, Article ID 254593, 10 pagesdoi:10.1155/2008/254593Research Article Global Behavior of the Components for the Second Order m-Point Boundary Value ProblemsYulian ... the global behavior of the components of nodal solutions of 1.8, 1.9and give a positive answer to the above question. However, when m-point boundary value condition 1.9 is concerned, the ... Global behavior of the components of nodal solutions of asymptotically linear eigenvalueproblems,” Applied Mathematics Letters, 2007.3 R. Ma and D. O’Regan, “Nodal solutions for second- order...
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báo cáo hóa học:" Research Article Asymptotic Behavior of Equilibrium Point for a Family of Rational Difference Equations" docx
... condition for the local stability of the difference equationxnk s1xnk−1 ··· skxn 0,n 0, 1, 2.43. The Main Results and Their ProofsIn this section, we investigate the globally ... conditionsx−m,x−m1, ,x1,x0 ∈ 0,μm1.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,li1Asi<B21−D/k ... Computations are performed using the software package Matlab 7.1.We have dealt with the problem of global asymptotic stability analysis for a class of nonlinear difference equation. The general sufficient...
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báo cáo hóa học:" Research Article Global Structure of Nodal Solutions for Second-Order m-Point Boundary Value Problems with Superlinear Nonlinearities" pot
... Corporation Boundary Value ProblemsVolume 2011, Article ID 715836, 12 pagesdoi:10.1155/2011/715836Research Article Global Structure of Nodal Solutions for Second- Order m-Point Boundary Value Problemswith ... of the components f or the second order m-point boundary value problems,” Boundary Value Problems, vol. 2008, Article ID 254593, 10 pages, 2008.6 R. Ma and Y. An, Global structure of positive ... considered.Next, we consider the eigenvalues of the linear problemLu λu, u ∈ E. 1.7We call the set of eigenvalues of 1.7 the spectrum of L and denote it by σL. The followinglemmas or similar...
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báo cáo hóa học:" Research Article Extremal Values of Half-Eigenvalues for p-Laplacian with Weights in L1 Balls" potx
... is the monotonicity of the half-eigenvalues on the weights a, b. The other is the infimum HFm,γr can be attained by some weights for any γ ∈ 1, ∞.Asconsequence 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 maximizers, of the extremal value ... extremal problems of eigenvalues of the p-Laplacian,” to appear in Transactions of the American Mathematical Society.11 M. Zhang, “Extremal values of smallest eigenvalues of Hill’s operators...
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Báo cáo hóa học: "Research Article Global Behavior for a Diffusive Predator-Prey Model with Stage Structure and Nonlinear" docx
... 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 ... α31α32 0, then 1.1 reduces to the system 1.4 of Part I.Recently, the work in 18–20 studied the existence, uniform boundedness, anduniform convergence of global solutions for the Lotka-Volterra ... Moreover, global asymptoticstability of the positive equilibrium point for 1.1 is proved by an important lemma of 21. The proof is complete and complement the uniform convergence theorem in18–20.2....
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Báo cáo hóa học: " Research Article Asymptotic Behavior of Solutions of Higher-Order Dynamic Equations on Time Scales" pptx
... ≤ GuT P.2.53 The rest of the proof is similar to that of Theorem 2.8, and the details are omitted. The proofis completed.Theorem 2.10. Assume that the function ft, u0, ,un−1 ... equations. Many otherinteresting time scales exist, and they give rise to many applications see 2. Not only the new theory of the so-called “dynamic equations” unifies the theories of differential ... pagesdoi:10.1155/2011/237219Research Article Asymptotic Behavior of Solutions of Higher -Order Dynamic Equations on Time ScalesTaixiang Sun,1Hongjian Xi,2and Xiaofeng Peng11College of Mathematics and Information...
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Báo cáo hóa học: " Research Article Asymptotic Behavior of a Periodic Diffusion System" pot
... estimates are crucial for the proof of the existence of the maximalperiodic 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 20especially, established the existence and uniqueness of the solutions of the ... establish the existence of the maximum periodicsolution and the asymptotic boundedness of the nonnegative solutions of the initial boundary value problem.1. IntroductionIn this paper, we consider the...
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Báo cáo hoa học: " Research Article Asymptotic Behavior of Impulsive Infinite Delay Difference Equations with Continuous Variable" docx
... andA2. In the following, we give the attractivity of the zero solution and the proof is similar tothat of Theorem 3.3.Corollary 3.5. If A1−A4 hold with I 0, then the zero solution of 2.4 ... 0inTheorem 3.3. It follows fromTheorem 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 observe t hat xt ≡ 0 is a solution of ... 3.35This implies that the conclusion of the theorem holds and the proof is complete.2 Advances in Difference Equationsthis paper is to study the asymptotic behavior of impulsive infinite delay...
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