application of second order partial differential equations
báo cáo hóa học:" Research Article Error Bounds for Asymptotic Solutions of Second-Order Linear Difference Equations II: The First Case" pot
... completed the estimate of the error bounds for asymptotic solutions to second order linear difference equations in the first case For the second case, we leave it to the second part of this paper: Error ... of Second- order Linear Difference Equation II: the second case In the rest of this paper, we would like to give an example to show how to use the results of this paper to obtain error bounds of ... problem of obtaining error bounds for these asymptotic solutions to 1.2 is still open The purpose of this and the next paper Error bounds for asymptotic solutions of second- order linear difference equations...
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Báo cáo sinh học: " Research Article Multiple Positive Solutions of Fourth-Order Impulsive Differential Equations with Integral Boundary Conditions and One-Dimensional p-Laplacian" ppt
... < ξ < L 3.27 Proof If 3.1 of H3 holds, similar to the proof of 3.7 , we can prove that Ty PC1 ≤ y PC1 y ∈ K, , y l PC1 3.28 If 3.14 and 3.15 of H4 hold, similar to the proof of 3.23 , we have ... solution y t , t ∈ J with property 3.17 Proof The proof is similar to that of Theorem 3.2 of Theorem 3.5 Assume that H1 , H2 , 3.1 of H3 and 3.14 and 3.15 of H4 hold In addition, letting f and Ik ... and Applications, vol 327, no 2, pp 854–868, 2007 M Feng and D Xie, “Multiple positive solutions of multi-point boundary value problem for secondorder impulsive differential equations, ” Journal of...
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Báo cáo hóa học: " Research Article Global Behavior of Solutions to Two Classes of Second-Order Rational Difference Equations Sukanya Basu and Orlando Meri" docx
... Dynamics of Second Order Rational Difference Equations, Chapman & c Hall/CRC, Boca Raton, Fla, USA, 2002 G Ladas, “Invariants for generalized Lyness equations, ” Journal of Difference Equations and Applications, ... the proof of Theorem 1.4 By considering the restriction of the map T of 1.15 to m∗ , M∗ , an application of the Schauder Fixed Point Theorem 17 gives that m∗ , M∗ contains the fixed point of T , ... Ladas, “On second- order rational difference equation—I,” Journal of Difference Equations and Applications, vol 13, no 11, pp 969–1004, 2007 A M Amleh, E Camouzis, and G Ladas, “On second- order rational...
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Báo cáo hoa học: " Research Article On Connection between Second-Order Delay Differential Equations and Integrodifferential Equations with Delay" pdf
... ψ is defined by 2.5 Proof In the proof we will use notation defined in the proof of Theorem 2.1 The existence and uniqueness of a solution of 1.11 , 2.1 is a consequence of Theorem 2.1 Thus, we ... investigate the problems of the existence, uniqueness and solution representation of 1.11 Problems related to oscillation/nonoscillation, stability and applications to second- order equations will be ... Advances in Difference Equations One of the methods used to study 1.1 is transforming the second- order delay differential equation to a first -order differential or integrodifferential equations with delay...
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Báo cáo hóa học: " Research Article On Periodic Solutions of Higher-Order Functional Differential Equations" ppt
... to one of the conditions of the lemma, admits estimate 2.18 Therefore, estimate 2.31 is valid 10 Boundary Value Problems Proof of the main results Proof of Theorem 1.1 Without loss of generality, ... all the conditions of Theorem 1.1 are fulfilled which guarantee the existence of at least one ω-periodic solution of 1.4 I Kiguradze et al 13 Proof of Corollary 1.4 Without loss of generality, it ... solutions of higher order systems,” Pacific Journal of Mathematics, vol 84, no 2, pp 275–282, 1979 G T Gegelia, “On boundary value problems of periodic type for ordinary odd order differential equations, ”...
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Báo cáo hóa học: " Research Article On the Spectrum of Almost Periodic Solution of Second-Order Neutral Delay Differential Equations with Piecewise Constant of Argument" ppt
... “On the spectrum of almost periodic solution of second order scalar functional differential equations with piecewise constant argument”,” Journal of Mathematical Analysis and Applications, vol ... Difference Equations 12 R Yuan, “On the spectrum of almost periodic solution of second- order differential equations with piecewise constant argument,” Nonlinear Analysis: Theory, Methods & Applications, ... differential equations and almost periodic flows,” Journal of Differential Equations, vol 5, no 1, pp 167–181, 1969 18 R Yuan, “Pseudo-almost periodic solutions of second- order neutral delay differential equations...
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quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order
... estimates of the gradients of solutions of quasilinear elliptic equations of the form (1) and their application to the proof of certain qualitative properties of solutions of these equations ... to the study of questions of solvability of main boundary value problems for degenerate and nonuniformly elliptic and parabolic equations of second order and to the investigation of differential ... degenerate equations We then establish local estimates of the gradients of solutions of equations of the form (1) by combining the use of certain methods characteristic of the technique of global...
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báo cáo hóa học:" Research Article Regularly Varying Solutions of Second-Order Difference Equations with Arbitrary Sign Coefficient" ppt
... Proceedings of the American Mathematical Society, vol 41, pp 110–116, 1973 ˇ a S Matucci and P Reh´ k, “Regularly varying sequences and second order difference equations, ” Journal of Difference Equations ... existence of a solution y ∈ NRV look for a solution of 1.1 in the form yk k−1 ψj j 1 j a of 1.1 Set ψk wj k ∞ j k pj − A We , 3.8 k ≥ a, with some a ∈ N In order that y is a nonoscillatory solution of ... space of sequences converging towards zero The following properties of h will play a crucial role in the proof The first two are immediate consequences of the discrete L’Hospital rule and of the...
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báo cáo hóa học:" Research Article Solutions and Green’s Functions for Boundary Value Problems of Second-Order Four-Point Functional Difference Equations" ppt
... N, we denote by xt an element of Cτ defined by xt k x t k , k ∈ −τ, Boundary Value Problems In this paper, we consider the following second- order four-point BVP of a nonlinear functional difference ... ≤ s ≤ T ⎪ ⎪ ⎪ ⎩ 2.15 Proof Consider the second- order two-point BVP −Δ2 u t − f t, u u T t ∈ 1, T , 2.16 0, Boundary Value Problems It is easy to find that the solution of BVP 2.16 is given by ... ) holds Then the second- order four-point BVP 2.13 has a unique solution which is given in 2.29 Proof We need only to show the uniqueness Obviously, w t in 2.29 is a solution of BVP 2.13 Assume...
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báo cáo hóa học:" Research Article Multiple Positive Solutions of a Singular Emden-Fowler Type Problem for Second-Order Impulsive Differential Systems" pdf
... for second order impulsive differential systems,” Nonlinear Analysis: Theory, Methods & Applications, vol 13, no 1, pp 75–85, 1989 S G Hristova and D D Ba˘nov, “Existence of periodic solutions of ... systems of differential ı equations with impulse effect,” Journal of Mathematical Analysis and Applications, vol 125, no 1, pp 192–202, 1987 E K Lee and Y.-H Lee, “Multiple positive solutions of a ... for secondorder impulsive differential systems,” Mathematical and Computer Modelling, vol 40, no 3-4, pp 307– 328, 2004 B Liu and J Yu, “Existence of solution of m-point boundary value problems of...
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Báo cáo sinh học: " Research Article Existence and Lyapunov Stability of Periodic Solutions for Generalized Higher-Order Neutral Differential Equations" potx
... kind of high -order neutral functional differential equation,” Journal of Mathematical Analysis and Applications, vol 326, no 2, pp 1161–1173, 2007 J Wu and Z Wang, “Two periodic solutions of second- order ... Analysis: Theory, Methods & Applications, vol 71, no 12, pp 6182–6193, 2009 J Shen and R Liang, “Periodic solutions for a kind of second order neutral functional differential equations, ” Applied Mathematics ... In general, most of the existing results are concentrated on lower -order neutral functional differential equations, while studies on higher -order neutral functional differential equations are rather...
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báo cáo hóa học:" Research Article Oscillation of Second-Order Mixed-Nonlinear Delay Dynamic Equations" pdf
... nonoscillation of forced second order dynamic equations, ” Pacific Journal of Mathematics, vol 230, no 1, pp 59–71, 2007 12 M Bohner and S H Saker, “Oscillation of second order nonlinear dynamic equations on ... criteria for second- order forced dynamic equations with mixed nonlinearities,” Advances in Difference Equations, vol 2009, Article ID 938706, 20 pages, 2009 D R Anderson, “Oscillation of second- order ... functional dynamic equations with delay and advanced arguments,” to appear in Journal of Difference Equations and Applications 10 A F Guvenilir and A Zafer, Second- order oscillation of forced functional...
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Báo cáo hóa học: " Research Article Inequalities among Eigenvalues of Second-Order Difference Equations with General Coupled Boundary Conditions" pptx
... in Difference Equations Y Wang and Y Shi, “Eigenvalues of second- order difference equations with periodic and antiperiodic boundary conditions,” Journal of Mathematical Analysis and Applications, ... Problems, vol of Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1964 Y Shi and S Chen, “Spectral theory of second- order vector difference equations, ” Journal of Mathematical ... which proves the first conclusion ¨ The second conclusion can be shown similarly Hence, the proof is complete Finally, we turn to the proof of Theorem 3.1 Proof of Theorem 3.1 By Propositions 3.3–3.8,...
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Báo cáo hóa học: " Research Article Sturm-Picone Comparison Theorem of Second-Order Linear Equations on Time Scales" ppt
... differential equations of second order, ” Annals of Mathematics, vol 65, pp 197–202, 1957 R Zhuang, “Sturm comparison theorem of solution for second order nonlinear differential equations, ” Annals of Differential ... comparison theorem of second- order differential equations see Section Remark 3.6 In the discrete case: μ t ≡ This result is the same as Sturm comparison theorem of second- order difference equations see ... differential equations of second order, ” Proceedings of the American Mathematical Society, vol 13, pp 603–610, 1962 W Leighton, “Some elementary Sturm theory,” Journal of Differential Equations, ...
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Báo cáo hóa học: " Research Article Existence Theorems of Periodic Solutions for Second-Order Nonlinear Difference Equations" pot
... for a certain class of second order differential equations, ” Journal of Differential Equations, vol 82, no 1, pp 15–27, 1989 13 M Marini, “On nonoscillatory solutions of a second- order nonlinear differential ... Journal of Mathematical Analysis and Applications, vol 179, no 2, pp 512–524, 1993 F Dannan, S Elaydi, and P Liu, “Periodic solutions of difference equations, ” Journal of Difference Equations and Applications, ... with Applications, vol 36, no 10–12, pp 11–26, 1998, Advances in difference equations, II 11 P J Y Wong and R P Agarwal, “Oscillation and monotone solutions of second order quasilinear difference equations, ”...
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Báo cáo hóa học: " Research Article On Complex Oscillation Property of Solutions for Higher-Order Periodic Differential Equations Zong-Xuan Chen and Shi-An Gao" pdf
... that the above proof remains valid if we interchange the roles of G j and g j as at the end of the proof of Lemma 2.6 The proof of Theorem 1.3 is completed Lemma for the proof of Theorem 1.6 Lemma ... every solution f ≡ of (1.2) satisfies (1.14) This completes the proof of Theorem 1.6 Proofs of corollaries Proof of Corollary 1.4 By Remark 2.7, we see that the hypotheses of Theorem 1.3 are satisfied ... function N1 (ρ,1/G) of G(ξ) in < |ξ | < ∞ satisfies log+ N1 (ρ,1/G) = O(logρ) So that u(ξ) is an entire function of finite order Secondly, we prove that h(ξ) is of finite order of growth Set W(ξ)...
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Báo cáo hóa học: " Research Article Existence Theorems of Periodic Solutions for Second-Order Nonlinear Difference Equations" doc
... for a certain class of second order differential equations, ” Journal of Differential Equations, vol 82, no 1, pp 15–27, 1989 13 M Marini, “On nonoscillatory solutions of a second- order nonlinear differential ... Journal of Mathematical Analysis and Applications, vol 179, no 2, pp 512–524, 1993 F Dannan, S Elaydi, and P Liu, “Periodic solutions of difference equations, ” Journal of Difference Equations and Applications, ... with Applications, vol 36, no 10–12, pp 11–26, 1998, Advances in difference equations, II 11 P J Y Wong and R P Agarwal, “Oscillation and monotone solutions of second order quasilinear difference equations, ”...
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Báo cáo hóa học: " PERIODIC SOLUTIONS OF SECOND-ORDER LIÉNARD EQUATIONS WITH p-LAPLACIAN-LIKE OPERATORS" pot
... solutions of forced nonlinear second order ordinary differential equations, Bulletin of the London Mathematical Society 18 (1986), no 2, 173–180 [7] J.-P Gossez and P Omari, Periodic solutions of a second ... nard equations e Motivated by the work of [13], in this paper we use new polar coordinates [13] to investigate the existence of periodic solutions for the second- order generalized Li´ nard e equations ... existence of a unique nontrivial periodic solution to a class of equations of Li´nard’s type, Journal of Differential Equae tions 46 (1982), no 3, 356–378 [12] P N Savel’ev, Dissipativity of the...
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Báo cáo hóa học: "OSCILLATION OF SECOND-ORDER NEUTRAL DELAY AND MIXED-TYPE DYNAMIC EQUATIONS ON TIME SCALES" pdf
... great deal of work on the oscillatory behavior of solutions of some second- order dynamic equations To the best of our knowledge, there is very little known about the oscillatory behavior of (NE) ... (3.14) i =n −h In the proof of Theorem 2.3, first (2.1) is reduced to a first -order delay dynamic equation in the form of (2.2) and then, by similar steps of the proof of well-known oscillation ... the oscillation of delay difference equations, Journal of Applied Mathematics and Simulation (1989), no 2, 101–111 [9] Y Sahiner, Oscillation of second- order delay differential equations on time...
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Báo cáo y học: "Modelling of oedemous limbs and venous ulcers using partial differential equations" pdf
... leg shape with an ulcer We utilise a mixture of PDEs of order four and six in order to model the surface shapes in question In order to generate a Page of (page number not for citation purposes) ... and a sixth order patch Figure surface data of an arm Scanned6 Scanned surface data of an arm representative smooth PDE surface shape, we extract a series of curves along the profile of the geometric ... form offunctionin 3-space TheThethe of a surfaceare all takenby the fourth order PDE Figure conditions defined in the to be curves conditions The shape of a surface generated by the fourth order...
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