Báo cáo hóa học: "PERIODIC SOLUTIONS OF NONLINEAR VECTOR DIFFERENCE EQUATIONS" ppt

... + T−1  j=0 U h (T, j +1)f ( j), (3.4) PERIODIC SOLUTIONS OF NONLINEAR VECTOR DIFFERENCE EQUATIONS M. I. GIL’ Received 31 January 2005; Accepted 7 September 2005 Essentially nonlinear difference equations in ... consider essentially nonlinear systems in a Euclidean space. We prove the existence of periodic solutions and derive the estimates for their norms. Let C n be the set...

Ngày tải lên: 22/06/2014, 22:20

... multiplicity results for periodic solutions of semilinear Duffing equations,JournalofDiffer ential Equations 105 (1993), no. 2, 364–409. [5] C. Fabry and D. Fayyad, Periodic solutions of second order differential ... Mawhin, Periodic solutions for nonlinear sy stems with p-Laplacian-like operators,JournalofDifferential Equations 145 (1998), no. 2, 367–393. [9] J.MawhinandJ.R.WardJr.,Pe...

Ngày tải lên: 22/06/2014, 22:20

... case of uniqueness, the dissipative system (1.1) admits at least 6 Dissipative systems of the implied τ-periodic solution of (1.1) or a lower estimate of the number of τ-periodic solutions of (1.1), ... Proceedings of the National Academy of Sciences of the United States of America 53 (1965), 1262–1264. [23] N. Levinson, Transformation theory of non-linear differential...

Ngày tải lên: 22/06/2014, 22:20

... (y,ay−x). The simplicity of T gives no hint of the startling complexity shown by scatter plots of some of the solutions. See Figures 4.1–4.4,below. 2. Qualitative b ehavior of solutions Henceforth, ... establish the periodicity of all solutions to (1.1)seems novel, elegant, and of potentially wider applicability. Without this method, we could not prove that solutions o...

Ngày tải lên: 22/06/2014, 22:20

... methods allow us to improve the previous results. 2. Proofs of the theorems We now give t h e proof of Theorem 1.1. Proof. Let X be the set of vector functions x(t)givenby(1.2) and described above. ... satisfying x 2 X = n  j=1   x j   2 H 1 . (2.1) Martin Schechter 7 The proof of Theorem 1.2 is similar to that of Theorem 1.1 with the exception of the inequality (2.8) res...

Ngày tải lên: 22/06/2014, 22:20

... is just the repetition of the proof of Lemma 3.2, we omit the details of its proof. With the aid of above preparations, now we will give the proof of Theorem 1.2. Proof of Theorem 1.2 By(1.8), ... similar to the proof of Lemma 3.1, so we omit the details of its proof. Lemma 3.4 Under the conditions of Theorem 1.2, F (x) satisfies the PS condition. Proof From the proof of Le...

Ngày tải lên: 20/06/2014, 04:20

... for the study of solutions to systems of nonlinear matrix equations involving contractive mappings. We first review the Thompson metric on the open convex cone P(n)(n ≥ 2), the set of all n×n Hermitian ... Duan, F: Positive defined solution of two kinds of nonlinear matrix equations. Surv Math Appl. 4, 179–190 (2009) 12. Hasanov, V: Positive definite solutions of the matri...

Ngày tải lên: 20/06/2014, 22:20

... et al. Advances in Difference Equations 2011, 2011:58 http://www.advancesindifferenceequations.com/content/2011/1/58 Page 3 of 12 RESEARCH Open Access Polynomial solutions of differential equations H ... On polynomial solutions of a class of linear differential equations of the second order. Bull A M S. 36, 77–84 (1930). doi:10.1090/S0002-9904-1930-04888-0 Azad et al. Advances...

Ngày tải lên: 20/06/2014, 22:20

... follows from ( 1 ) which are appeared in the proof of Theorem 1.2. Then the proof of Theorem 1.3 is completed. □ Proof of Theorem 1.4. From the proof of Theorem 1.1, we know that  is coercive which ... multiplicity of periodic solution for a class of non-autonomous second-order systems with linear nonlinearity. Nonlinear Anal. 60, 325–335 (2005) 12. Wang, Z, Zhang, J: Periodic...

Ngày tải lên: 21/06/2014, 00:20