Báo cáo hóa học: " PERIODIC SOLUTIONS OF SECOND-ORDER LIÉNARD EQUATIONS WITH p-LAPLACIAN-LIKE OPERATORS" pot

... 2 Positive solutions of difference equations Recently, the existence of positive solutions of finite difference equations with different boundary value conditions is ... (1.13) POSITIVE SOLUTIONS OF FUNCTIONAL DIFFERENCE EQUATIONS WITH p-LAPLACIAN OPERATOR CHANG-XIU SONG Received 18 October 2005; Accepted 10 January 2006 The author studies the boundary value problems with...

Ngày tải lên: 22/06/2014, 22:20

... θ||sinθ| (4−p)/p PERIODIC SOLUTIONS OF SECOND-ORDER LIÉNARD EQUATIONS WITH p-LAPLACIAN-LIKE OPERATORS YOUYU WANG AND WEIGAO GE Received 12 April 2005; Accepted 10 August 2005 The existence of periodic solutions ... for periodic solutions of semilinear Duffing equations, JournalofDiffer ential Equations 105 (1993), no. 2, 364–409. [5] C. Fabry and D. Fayyad, Periodic...

Ngày tải lên: 22/06/2014, 22:20

... 1,weobtainobvi- ously again a τ -periodic solution x 0 (· )of( 1.1)withx 0 (0) ∈ Ᏸ \ intA and, in the case of uniqueness, three τ-per iodic solutions of (1.1). PERIODIC SOLUTIONS OF DISSIPATIVE SYSTEMS REVISITED JAN ... Proceedings of the National Academy of Sciences of the United States of America 53 (1965), 1262–1264. [23] N. Levinson, Transformation theory of non-lin...

Ngày tải lên: 22/06/2014, 22:20

... used to 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 of the special case ... (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...

Ngày tải lên: 22/06/2014, 22:20

... Stability and periodicity of difference equations with finite delay, Funkcialaj Ekvacioj. Serio Internacia 37 (1994), no. 3, 401–413. [3]M.I.Gil’ ,Periodic solutions of abstract difference equations, ... existence of periodic solutions of discrete difference equations, Uzbekski ˘ ı Matematicheski ˘ ı Zhurnal (1995), no. 3, 88–90 (Russian). [10] Kh. Turaev, On the existence an...

Ngày tải lên: 22/06/2014, 22:20

... 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. It is a Hilbert space with norm satisfying x 2 X = n  j=1   x j   2 H 1 . ... proof of Theorem 1.2 is similar to that of Theorem 1.1 with the exception of the inequality (2.8) resulting from Hypothesis (2). In its p...

Ngày tải lên: 22/06/2014, 22:20

... 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 ... c]. Proof The existence and uniqueness of the solution to (30) follows from classical the- orems on Carathéodory solutions of ordinary differential equations. We con...

Ngày tải lên: 21/06/2014, 02:20

... in the presence of minor amount of EDTA were favorable for the formation of 513MOS nanowires with high aspect ratio. Conclusion 513MOS nanowires with a length of 20–60 lm and a diameter of 60–300 nm ... ways of MgSO 4 Á 7H 2 O and NH 4 OH solutions at room temperature followed by hydrothermal treatment of the slurries at 150 ° C for 12 h with or without EDTA. 513MOS nano...

Ngày tải lên: 22/06/2014, 01:20

... give approximate solutions which consist of outer solutions and boundary layer correction solutions. Notice that in general this method cannot be extended for the general case of time-variant ... uniqueness of the solution of problem (P ε ), and successive approximations of this solution, obtained by a simple procedure. A proof is given of uniform convergence of the iterati...

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...

Ngày tải lên: 20/06/2014, 04:20