Báo cáo hóa học: "PERIODIC SOLUTIONS OF DISSIPATIVE SYSTEMS REVISITED" potx

... 8 Dissipative systems of approximating differential systems. If these systems are assumed to be dissipative, then they admit, according to Theorem 1.1, τ-periodic solutions. The desired ... τ-periodic solution of (1.1) can be so obtained, by the diagonalization argument, as a uniform limit of a selected sequence of τ-periodic solutions of approximating systems. In case...

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 ... existence of a unique nontrivial periodic solution to a class of equations of Li ´ enard’s type,JournalofDiff erential Equa- tions 46 (1982), no. 3, 356–378. [12] P. N....

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

... for the existence of periodic solutions and solution estimates are derived. Our main tool is a combined usage of the recent estimates for matrix-valued functions with the method of majorants. Copyright ... 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 of all...

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. ... 0. (1.13) PERIODIC SOLUTIONS OF SECOND-ORDER NONAUTONOMOUS DYNAMICAL SYSTEMS MARTIN SCHECHTER Received 13 March 2006; Rev ised 10 May 2006; Accepted 15 May 2006 We study the existen...

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

... include a proof for the readers’ convenience and because it is the main point in computation of norms of eigenfunctions. Prop osition 2.6 [8, p. 306] If {P n } n =0,1,2 is a sequence of orthogonal ... orthogonality of eigen- functions of different degrees. Now, from the differential equation, determining the leading three coefficients of every P n and using Equation 2.4 leads to...

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 ... completes the proof. □ 3 Proof of main results For the sake of convenience, we will denote various positive constants as C i , i =1,2, 3, Now, we are ready to proof our main resul...

Ngày tải lên: 21/06/2014, 00:20

... of first-order partial differential equations, including questions such as estimates of solutions of initial problems, estimates of domains of solutions, estimates of the difference between solutions ... Journal of Inequalities and Applications 2011, 2011:15 http://www.journalofinequalitiesandapplications.com/content/2011/1/15 Page 3 of 20 functions of one variable, whi...

Ngày tải lên: 21/06/2014, 02:20