and fourth order dpw sawtooth oscillators

... can refer to 3–5 and the references therein Recently, nonhomogeneous BVPs have attracted many authors’ attention For instance, Ma 6, and L Kong and Q Kong 8–10 studied some second -order multipoint ... unique solution and then studied the dependence of this solution on the parameters λ and μ Sun 11 discussed the existence and nonexistence of positive solutions to a class of third -order three-point ... BVP consisting of the fourth- order differential equation: u4 f t, u , t ∈ 0, 1.5 and the four-point nonhomogeneous boundary conditions αu − βu au ξ1 − bu ξ1 where ≤ ξ1 < ξ2 ≤ and λi assumptions:...

Ngày tải lên: 21/06/2014, 11:20

... |s| sufficiently large and which satisfy the relation eωk sx yk x, s υ uv,k x sv O s8 , k 2.2 1, 2, 3, , where the numbers ωk are the fourth roots of unity, that is, ω1 −ω4 i and ω2 −ω3 In general, ... roots sk,1 and sk,2 , k 1, , of 3.10 and 3.11 , respectively, where N is a big positive integer sk,1 sk,2 2ki 32π 2k 32π π q2 t dt 2ki π q2 t dt 2k From the relations 3.12 , 3.13 and the relations ... 2kx O Case Assume that q x ∈ C 0, π and the conditions q π − q 0 and q π − q / hold Based on the asymptotic expressions of the fundamental solutions of 1.1 and the asymptotic formulas for eigenvalues...

Ngày tải lên: 21/06/2014, 11:20

... , 0, ∞ and may be singular at t or t 1; f, g : 0, × P \ {θ} × 0; , bi , ci , and P \ {θ} → P are continuous and may be singular at t 0, 1, u 0, and u di ∈ 0, ∞ , and ρi ci di bi ci > 0, and mi ... corresponding to clamped and hinged ends and many nonlocal boundary conditions and established excellent existence results for multiple positive solutions of fourth- order nonlinear equations ... · < tm < tm 1, Δx |t tk x tk − x t− , where x tk and x t− represent the right-hand limit and left-hand k k limit of x t at t tk , respectively, and g, h ∈ L1 0, is nonnegative For the case of...

Ngày tải lên: 21/06/2014, 16:20

... Existence and multiplicity of solutions for a fourth- order elliptic equation Fanglei Wang∗1 and Yukun An2 College Department of Science, Hohai University, ... nontrival solutions for a fourth- order elliptic equation   ∆ u − M  | u|2 dx ∆u = f (x, u), inΩ, Ω    u = ∆u = 0, on ∂Ω by using the mountain pass theorem Keywords: fourth- order elliptic equation; ... where a(x) ∈ Lq (Ω), b ∈ R and < p < N +4 N −4 if N > and < p < ∞ if N ≤ and q + p = 1; (H4) f (x, t) = o(|t|) as t → uniformly for x ∈ Ω ; (H5) There exists a constant Θ > and R > 0, such that ΘF...

Ngày tải lên: 21/06/2014, 17:20

... uniqueness and iteration of positive solutions of discrete fourth- order equation under Lidstone boundary conditions We would like to mention some results of Anderson and Minhos 11 and He and Su 12 ... D R Anderson and F Minhos, “A discrete fourth- order Lidstone problem with parameters,” Applied ´ Mathematics and Computation, vol 214, no 2, pp 523–533, 2009 12 T He and Y Su, “On discrete fourth- order ... of fourth- order difference equations,” Applied Mathematics and Computation, vol 161, no 1, pp 139–148, 2005 10 J V Manojlovi´ , “Classification and existence of positive solutions of fourth- order...

Ngày tải lên: 21/06/2014, 18:20

... of certain fourth order nonlinear difference equations,” Journal of Mathematical Analysis and Applications, vol 322, no 2, pp 930–956, 2006 13 E Thandapani and I M Arockiasamy, Fourth- order nonlinear ... “Existence and uniqueness theorems for fourth- order boundary value problems,” Journal of Mathematical Analysis and Applications, vol 116, no 2, pp 415–426, 1986 C P Gupta, “Existence and uniqueness ... “On fourth order boundary value problems arising in beam analysis,” Differential and Integral Equations, vol 2, no 1, pp 91–110, 1989 C P Gupta, “Existence and uniqueness theorems for some fourth...

Ngày tải lên: 21/06/2014, 20:20

... Cheng, On a class of fourth- order linear recurrence equations, Int J Math Math Sci (1984), no 1, 131–149 J R Graef and E Thandapani, Oscillatory and asymptotic behavior of fourth order nonlinear delay ... 15–24 E Thandapani and I M Arockiasamy, Oscillatory and asymptotic properties of solutions of nonlinear fourth order difference equations, Glas Mat Ser III 37(57) (2002), no 1, 119–131 J Yan and B ... Schmeidel, On the solutions of fourth order difference equations, Rocky Mountain J Math 25 (1995), no 4, 1485–1499 E Schmeidel, Nonscillation and oscillation properties for fourth order nonlinear difference...

Ngày tải lên: 23/06/2014, 00:20

... Read the passage and answer the questions below: When I was twelve, my family moved to the city At first, everything was strange and difficult to me Life in the city is always busy and the people ... Certainly 34 Let me help you the house d Oh, have we? I’ll go and get some milk What you know about the Sun? e It rises in the East and set in the 5West I’m bored f Yes, I’d love to 67 Where is ... a hurry Lots of bikes, motorbikes, cars and buses coming from every direction scared me Now I get used to the life in the city I am used to the noise and busy city traffic I’m no longer afraid...

Ngày tải lên: 09/07/2013, 01:26

...    be open and assume that Denition Let we say that equals up to order if partial derivatives of orders up to agree at the origin If order , we denote that by For equals and all up to $ ... effect (Makino and Berz, 2000), and high-dimensional veried quadrature (Makino and Berz, 1996; Berz, 2000) e" " hXxg" 4A Ê "  dĂ 44"     ăfe Ă be a box with Let be a ) and be an open ... all terms of of orders up to (and including) and by a bound of the range of over the domain box Then, the antiderivation of Taylor models is given by the following denition (Berz and Makino, 1998;...

Ngày tải lên: 12/01/2014, 21:46

... that landscape itself, and the symbols by which the law is represented carry their own history and significance So, in order to understand the law, it is necessary to have some understanding ... dilapidated, patched and altered during the succession of ages by a thousand additions and combinations' and so on Sousa Santos 1987, p 282 4 Criminal law, tradition and legal order time been taken ... exercised and boldly defended' now, 'we believe it to be ridiculous in negation and tyrannous in exercise, and indicative not of health or energy, but of the feverishness and weakness and disorder...

Ngày tải lên: 30/03/2014, 02:20

... adjacent words (or characters) when retrieving units of collocation and the co-occurrence frequencies and word order between a key string and other strings when retrieving collocations Through the method, ... Combine stri and strj when they overlap or adjoin each other and the following inequation is satisfied: freq(stri, strj ) freq(stri) > Tratio (4) • Filter out stri if strj subsumes stri and the following ... the languages without word delimiters, and for the other languages as well 2.2 Examine how often each possible combinations of str~ and stri co-occurs, and extract stri if the frequency exceeds...

Ngày tải lên: 31/03/2014, 21:20

Ngày tải lên: 24/04/2014, 17:17

... Hence, it is important to study the LCR and ADF in addition to the PDF and CDF of the instantaneous channel capacity in order to meet the increasing demand for high data rates in mobile communication ... and the CDF FC (r) of the capacity C(t) of N ∗Nakagami-m channels are presented in Figures and 3, respectively Also, the approximation results obtained in (23) and (24) are shown in Figures and ... relays can generally be classified into two types, namely amplify -and- forward (or non-regenerative) relays [9, 10] and decode -and- forward (or regenerative) relays [9, 11] The relay nodes in multihop...

Ngày tải lên: 20/06/2014, 20:20

... the single fourth order elliptic problem to that of the fourth order elliptic system Our main results are as follows: 11 b −a THEOREM 1.1 Suppose that ab ≠ and det = Let lk

Ngày tải lên: 20/06/2014, 22:20

... hE , γ2 , Γ2 , and ρ and it does not depend on the boundary conditions Existence and Location Result In the presence of an ordered pair of lower and upper functions, the existence and location ... Differential and Integral Equations, vol 4, no 2, pp 397–410, 1991 F Minhos, T Gyulov, and A I Santos, “Existence and location result for a fourth order boundary ´ value problem,” Discrete and Continuous ... 2.2 By integration, from iii and 2.1 , we obtain α t ≤β t , α t ≤β t , ∀t ∈ 0, , 2.2 that is, lower and upper functions, and their first derivatives are also well ordered To have an a priori estimate...

Ngày tải lên: 21/06/2014, 05:20

... 6, pp 1069–1078, 2003 X.-L Liu and W.-T Li, “Existence and multiplicity of solutions for fourth- order boundary value problems with three parameters,” Mathematical and Computer Modelling, vol 46, ... Mathematics and Computation, vol 168, no 2, pp 1219–1231, 2005 10 C Pang, W Dong, and Z Wei, “Multiple solutions for fourth- order boundary value problem,” Journal of Mathematical Analysis and Applications, ... vol 314, no 2, pp 464–476, 2006 Fixed Point Theory and Applications 11 11 Z Wei and C Pang, “Positive solutions and multiplicity of fourth- order m-point boundary value problems with two parameters,”...

Ngày tải lên: 21/06/2014, 07:20

... by Corduneanu 14 and Agarwal and O’Regan 15 Recently, Zhang et al 13 studied the existence and nonexistence of symmetric positive solutions for the following nonlinear fourth- order boundary value ... the existence and uniqueness of solutions for some fourth- order and k, n − k conjugate boundary value problems when f t, u, v q t g u h v , where g : 0, ∞ −→ 0, ∞ is continuous and nondecreasing, ... of Shandong Province Higher Educational Science and Technology Program no J10LA53 and the National Natural Science Foundation of China no 10971179 References X Du and Z Zhao, “Existence and uniqueness...

Ngày tải lên: 21/06/2014, 11:20

... NWNU-KJCXGCSK0303-23, and NWNU-KJCXGC-03-69 References R P Agarwal and Y M Chow, “Iterative methods for a fourth order boundary value problem,” Journal of Computational and Applied Mathematics, ... Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997 R Ma, “Existence of positive solutions of a fourth- order boundary value problem,” Applied Mathematics and ... interior nodal (i.e., nondegenerate) zeros in 0, and are positive near t 0, −Sk , and Sk Sk ∪ S− They are disjoint and open in E Finally, let Φ± R × S± and set S− k k k k Φk R × Sk The results of...

Ngày tải lên: 21/06/2014, 16:20

... term f not only involve with the first -order and the second -order derivatives explicitly, but also may be allowed to change sign and may be singular at t = and/ or t = Moreover, some stronger conditions ... theory in cone and constructing some available integral operators together with approximating technique They guarantee the existence of at least one positive solution for nonlinear fourth- order semipositone ... may take negative values and the nonlinearity may be sign-changing Firstly, we employ a exchange technique and construct an integral operator for the corresponding second -order multi-point boundary...

Ngày tải lên: 21/06/2014, 17:20

... solutions and we note no use was made of global results on bifurcation from infinity Recently 10 Wei and Pang studied the existence and multiplicity of nontrivial solutions for the fourth order m-point ... least 2k nontrivial solutions Theorem 3.2 Suppose (H1) and (H2) hold and one of (H3) and (H4) hold Suppose there exists two integers i0 and j0 such that μ20 i a1 Then BVP 1.1 has at least i0 ... has 2i0 nontrivial solutions {viν }i0 in which − v1 and v1 are positive and negative solutions, respectively On the other hand, by 3.33 , 3.35 , and Lemma 3.5 one can obtain ν Dj ∩ {1} × Y \ B R...

Ngày tải lên: 21/06/2014, 20:20