solving a second order equation

... equations Nauk Dumka, Kiev, 284 (1984) (Russian) 31 Yakubov, S, Yakubov, Ya: Differential-Operator Equations Ordinary and Partial Differential Equations Chapman and Hall/ CRC, Boca Raton, 568 ... interpretation, and modification of the initial version of this study Author details Department of Differential Equation, Institute of Mathematics and Mechanics-Azerbaijan National Academy of ... Walter considers a scalar Sturm-Liouville problem with an eigenvalue parameter l in the boundary conditions He shows that one can associate a self-adjoint operator with that by finding a suitable...

Ngày tải lên: 21/06/2014, 02:20

... Initial and boundary value problems of ordinary differential equations play an important role in many fields Various applications of boundary to physical, biological, chemical, and other branches ... Solving singular second- order initial/boundary value problems in reproducing kernel Hilbert space Er Gao*, Songhe Song** and Xinjian Zhang*** Department of Mathematics and Systems ... of applied mathematics are well documented in the literature The main idea of this paper is to present a new algorithm for computing the solutions of singular second- order initial/boundary value...

Ngày tải lên: 20/06/2014, 20:20

... Poltavskii and G N Vaniko, HYpersingular Integral Equations and Their Applications, CRC, 2004 [4] P A Martin, Exact solution of a simple hypersingular integral equation, Fournal of Integral Equations ... integral equations, Chapman & Hall / CRC Press, Boca Raton, 1999, 226 p [7] Nguyen Van Ngoc, On the solvability of dual integral equations involving Fourier Transforms, Acta Math Vietnamica, 13(2)(1988), ... eF˘ , SOLVING A DUAL INTEGRAL EQUATION Reduction to a hypersingular integral equation The aim of this Section is to propose a method for reducing the dual integral equation (2.13) to an hypersingular...

Ngày tải lên: 23/04/2015, 10:02

... MRS, Ladas, G: Dynamics of Second Order Rational Difference Equations, with Open Problems and Conjectures Chapman and Hall/CRC, London (2002) xn−1 Amleh, AM, Georgia, DA, Grove, EA, Ladas, G: ... Global asymptotic stability of a higher order rational difference equation J Math Anal Appl 330, 462–466 (2007) doi:10.1016/j.jmaa.2006.07.096 12 Sun, T, Xi, H: Global attractivity for a family ... behavior of a higher -order rational difference equation Adv Differ Equ 2006, (2006) Article ID 27637 Rhouma, MB, El-Sayed, MA, Khalifa, AK: On a (2, 2)-rational recursive sequence Adv Differ Equ...

Ngày tải lên: 20/06/2014, 22:20

... pp 60–82, Coll Judea Samaria, Ariel, Israel, 1993 Y Domshlak and I P Stavroulakis, “Oscillations of first -order delay differential equations in a critical state,” Applicable Analysis, vol 61, no ... 2008 G E Chatzarakis, R Koplatadze, and I P Stavroulakis, “Oscillation criteria of first order linear difference equations with delay argument,” Nonlinear Analysis: Theory, Methods & Applications, ... 00216 30503 and MSM 00216 30529 References R P Agarwal and A Zafer, “Oscillation criteria for second- order forced dynamic equations with mixed nonlinearities,” Advances in Difference Equations, vol...

Ngày tải lên: 21/06/2014, 18:20

... Scientiarium Naturalium Universitatis Masarykianae Brunensis Mathematica, vol 12, Masaryk University, Brno, 2003 I T Kiguradze and B L Shekhter, Singular boundary value problems for second- order ordinary ... 125–126 ˇ S Schwabik, M Tvrd´ , and O Vejvoda, Differential and Integral Equations Boundary Value y Problems and Adjoints, D Reidel, Dordrecht, 1979 S Mukhigulashvili: A Razmadze Mathematical Institute, ... Corollary 2.6 The validity of this assertion follows immediately from Corollary 2.5 (a) Acknowledgment This paper was prepared during the author’s stay at the Mathematical Institute of the Academy...

Ngày tải lên: 23/06/2014, 00:20

... empirical constants, κ0, and Psat, from the experimental data Using C1 = 1/κ0, obtained from equation (19), one can calculate A, at any value of A, using the equation for A Discussion Basic case ... product at A It decreases rapidly as (1 /A2 ) Equation (6) becomes p= A 1 + A k Psat (15) The initial slope is κ0, and Psat is the limiting rate of enzyme catalysis when saturated with A Increasing ... and (Ab)sat can be obtained directly by using a standard linear transformation of the data plot, see the enzyme kinetics case, equation (19) This gives a plot of (A/ Ab) versus A, with a slope...

Ngày tải lên: 13/08/2014, 16:20

... a e r b II Kaaaanauei sue (A, b)-annunTaaecaHe ypaaaexlta r n a a a Hexoropbte aaanuTUVecxue cpeAcTBa, ttcnonbayeM ie npa nccneAo- 80 aaHHa paapemHMOCra xpaeaaix aaAaa Ann (A, b)-an7Ianraaecxnx ... caa6biM nupoweaneM 175 179 179 181 § Ocaoaubie t4yaxgnoaanbabie npoCTpaacTBa, ceaaanabte c obi ea xpaeaoa aaAanea Ana (A, 0, m, m)-napa6onagecxnx ypaBHeana § 06tgaa xpaeaaa aaAa ... n (A, 0)-napa6onn9ecxae ypasaeaaz r n a B a (A, 0)-aiinnirrngecxue ypaBaeana § 061gaii xpaeaaa aaAaga in (A, 0, m, m)-annanragecxnx ypaBaeana § (A, 0)-annmrrngecxae ypasaeaaa co...

Ngày tải lên: 31/05/2014, 01:37

... a, b ∈ Ì and a ≤ b, then μ ( [a, b)) = b − a and μ ( (a, b)) = b − σ (a) (iii) If a, b ∈ Ì\{max Ì} and a ≤ b, then μ ( (a, b]) = σ (b) − σ (a) and μ ( [a, b]) = σ (b) − a Li and Shu Advances in ... Banach spaces and preliminary results, and then we illustrate and prove some important lemmas and theorems Definition 3.1 Let × and Y be Banach spaces A linear operator L : Dom L ⊂ X ® Y is called ... with Riemann-Stieltjes Δ-integral conditions for second- order dynamic equations on time scales at resonance Advances in Difference Equations 2011 2011:42 Submit your manuscript to a journal and benefit...

Ngày tải lên: 20/06/2014, 22:20

... of Mathematical Analysis and Applications, vol 333, no 1, pp 505–522, 2007 S H Saker, D O’Regan, and R P Agarwal, “Oscillation theorems for second- order nonlinear neutral delay dynamic equations ... Computational and Applied Mathematics, vol 141, no 1-2, pp 1–26, 2002 R P Agarwal, D O’Regan, and S H Saker, “Oscillation criteria for second- order nonlinear neutral delay dynamic equations,” Journal ... differential equations with delayed argument,” International Journal of Differential Equations, vol 2010, Article ID 181784, 15 pages, 2010 R P Agarwal, D R Anderson, and A Zafer, “Interval oscillation...

Ngày tải lên: 21/06/2014, 05:20

... both cases, the Poincare mapping P always have invariant curves for being sufficient small Since ⇔ λ 1, we know that for any λ 1, there is an invariant curve of the Poincare mapping, which guarantees ... Pioncar´ map, the author obtained the existence of quasi-periodic solutions e and the boundedness of all solutions Then the result is generalized to a class of p-Laplacian differential equation. Yang ... system and then use a twist theorem of area-preserving mapping to the Pioncar´ map e The above differential equation essentially possess Hamiltonian structure It is well known that the Hamiltonian...

Ngày tải lên: 21/06/2014, 07:20

... 2 Advances in Difference Equations Differential equations with a small parameter < ε multiplying the highest order derivatives are called singularly perturbed differential equations Typically, ... vol 16 of Applied Mathematics, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2000 Advances in Difference Equations 13 H.-G Roos, M Stynes, and L Tobiska, Robust Numerical Methods for Singularly Perturbed ... small parameter, of a difference scheme for an ordinary differential equation, ” Computational Mathematics and Mathematical Physics, vol 35, no 11, pp 1417–1422, 1995 G F Sun and M Stynes, A uniformly...

Ngày tải lên: 21/06/2014, 11:20

... a0 − a1 /n − l n |} is a constant Equation 4.14 is an inhomogeneous second- order linear difference equation; its solution takes the form of a particular solution added to an arbitrary linear combination ... Breach, Amsterdam, The Netherlands, ¨ 1997 10 C M Bender and S A Orszag, Advanced Mathematical Methods for Scientists and Engineers, International Series in Pure and Applied Mathematics, McGraw-Hill ... q−p n α1 α1 A n2 f1 n , 4.6 where A −1 p−q 2b1 −p b0 b1 a1 − −p b0 a0 is a constant and n3 |f1 n | equation a1 a0 q a1 2a0 b1 −p b0 a1 −1 a0 4.7 q−3 , B B is a constant , from Lemma 2.2, we know...

Ngày tải lên: 21/06/2014, 11:20

... Matucci and P Reh´ k, Second order linear difference equations and Karamata sequences,” International Journal of Difference Equations, vol 3, no 2, pp 277–288, 2008 V Mari´ , Regular Variation and ... Let A ∈ −∞, 1/4 and denote by < , the real roots of the quadratic equation √ − A Note that − 1 − 4A > 0, − sgn , and > , sgn A Theorem 3.1 Equation 1.1 is nonoscillatory and has a fundamental ... Journal of Difference Equations and Applications, vol 14, no 1, pp 17–30, 2008 J Jaroˇ and T Kusano, “Self-adjoint differential equations and generalized Karamata functions,” s Bulletin Classe...

Ngày tải lên: 21/06/2014, 11:20

... help, careful reading and editing, valuable comments and suggestions References R P Agarwal, Difference Equations and Inequalities: Theory, Methods, and Application, vol 228 of Monographs and Textbooks ... in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 2nd edition, 2000 R P Agarwal, S R Grace, and D O’Regan, Oscillation Theory for Difference and Functional Differential Equations, ... Equations, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000 R P Agarwal, E Thandapani, and P J Y Wong, “Oscillations of higher -order neutral difference equations,” Applied Mathematics Letters,...

Ngày tải lên: 21/06/2014, 11:20

... Berlin, Germany, 1998 K Yosida, Functional Analysis, Classics in Mathematics, Springer, Berlin, Germany, 1995 F Ammar-Khodja, A Benabdallah, J E Munoz Rivera, and R Racke, “Energy decay for Timoshenko ... Journal of Differential Equations, vol 194, no 1, pp 82–115, 2003 F Alabau-Boussouira and P Cannarsa, A general method for proving sharp energy decay rates for memory-dissipative evolution equations,” ... memory,” Journal of Functional Analysis, vol 254, no 5, pp 1342–1372, 2008 C M Dafermos, “An abstract Volterra equation with applications to linear viscoelasticity,” Journal of Differential Equations,...

Ngày tải lên: 21/06/2014, 11:20

... Science Foundation of Naval Aeronautical and Astronautical University References M J Gai, B Shi, and D C Zhang, “Boundary value problems for second- order singular functional differential equations,” ... Deng and H Shi, “On boundary value problems for second order nonlinear functional difference equations,” Acta Applicandae Mathematicae, vol 110, no 3, pp 1277–1287, 2009 S K Ntouyas, Y G Sficas, and ... Chinese Annals of Mathematics, vol 2 3A, no 6, pp 1–10, 2001 Chinese Y Guo and J Tian, “Two positive solutions for second- order quasilinear differential equation boundary value problems with sign changing...

Ngày tải lên: 21/06/2014, 11:20

... } Then AT , ≤ is bounded Define A { λ, μ ∈ R2 \ { 0, } | 3.20 has a positive solution at λ, μ } Then A / ∅ by Lemma 3.4 and A, ≤ is a partially ordered set Lemma 3.6 Assume D1 ∼ D6 Then A, ≤ is ... ≥ A u, v > u, v , 3.11 and by Theorem 2.6, Tλ,μ has a fixed point in K ∩ Ω2 \ Ω1 Second, consider case λ > and μ Taking c1 , ηλ , m1 , and m2 as above and using the same computation, we may ... contradicts to Lemma 3.5 and the proof is done Lemma 3.7 Assume D1 ∼ D6 Then every nonempty chain in A has a unique supremum in A Proof Let C be a chain in A Without loss of generality, we may...

Ngày tải lên: 21/06/2014, 11:20

... Oscillation criteria for second- order nonlinear neutral difference equations of mixed type Ethiraju Thandapani∗1, Nagabhushanam Kavitha1 and Sandra Pinelas2 Ramanujan Institute for Advanced Study ... Mathematics, University of Madras, Chennai 600 005, India Departamento de Matem´tica, Universidade dos A ores, a c Ponta Delgada, Portugal ∗ Corresponding author: ethandapani@yahoo.co.in Email ... ethandapani@yahoo.co.in Email addresses: NK: kavitha snd@hotmail.com SP: sandra.pinelas@gmail.com Abstract Some oscillation criteria are established for the second order nonlinear neutral difference equations of...

Ngày tải lên: 21/06/2014, 17:20