LINEAR DIFFERENTIAL EQUATIONS LDE OF SECOND AND HIGHER ORDER

[22] A. S. Vatsala and J. Yang, “Monotone iterative technique for semilinear elliptic systems,” Bound-ary Value Problems, vol. 2005, no. 2, pp. 93–106, 2005.[23] Z. Drici, F. A. McRae, and J. Vasundhara Devi, “Monotone iterative technique for periodicboundary value problems with causal[r]

GENERALIZED QUASILINEARIZATION METHODAND HIGHER ORDER OF CONVERGENCE FORSECOND-ORDER BOUNDARY VALUE PROBLEMSTANYA G. MELTON AND A. S. VATSALAReceived 24 March 2005; Revised 13 September 2005; Accepted 19 September 2005The method of generalized quasilineariza[r]

x→0+( f (x)/x), g0:= limx→0+(g(x)/x), f∞:= limx→∞( f (x)/x), andg∞:= limx→∞(g(x)/x) exist as real numbers.There is an ongoing flurry of research activities devoted to positive solutions of dy-namic equations on time scales (see, e.g., [1–7]). This work entails an extension of<[r]

3 Y C. Li and S Y. Shaw, “On local α-times integrated C-semigroups,” Abstract and Applied Analysis,vol. 2007, Article ID 34890, 18 pages, 2007.4 Y C. Li and S Y. Shaw, “On characterization and perturbation of local C-semigroups,” Proceedings ofthe American Math[r]

x)2+ay leads to a first-order separable equation: wy= 2f(w)+a.References for Chapter T5Kamke, E., Differentialgleichungen: L¨osungsmethoden und L¨osungen, I, Gew¨ohnliche Differentialgleichungen,B. G. Teubner, Leipzig, 1977.Murphy, G. M., Ordinary Differential Equations and<[r]

Table 6. Total times of Red - Black SOR method and Jacobi method.N 60 120 180 240 300SOR(seconds) 1 2 7 12 19Jacobi (seconds) 4 45 200 720The Red - Black SOR method is clearly the fastest one in terms of serial time and the numberof iterations.Table 1,3,4 show that when t[r]

generating operators and optimal controls,” to appear in Optimization.[12] Y. Peng and X. Xiang, “Necessary conditions of optimality for second order nonlinear evolutionequations on Banach spaces,” in Proceedings of the 4th International Conference on Impuls[r]

.(12.7.2.4)If the case a = b = c, where system (12.7.2.2) can be integrated directly, does not take place, the above twofirst integrals (12.7.2.3) and (12.7.2.4) are independent. Hence, using them, one can express y2and y3in termsof y1and then substitute the resulting expressions into the first[r]

x, C1)=0, G(y, ψy)=C1.On solving these equations for the derivatives, we obtain linear separable equations, whichare easy to integrate.References for Chapter T7Kamke, E., Differentialgleichungen: L¨osungsmethoden und L¨osungen, II, Partielle DifferentialgleichungenErster Ordnu[r]

2790, 2008.28 M. Pei and S. K. Chang, “A quasilinearization method for second-order four-point boundary valueproblems,” Applied Mathematics and Computation, vol. 202, no. 1, pp. 54–66, 2008.29 B. Ahmad, “Approximation of solutions of the forced Duffing equ[r]

[1] Trần Quốc Chiến (2008), Giáo trình Phần mềm toán học, ĐH ĐN. [2] Phạm Huy Điển, Đinh Thế Lục, Tạ Duy Phượng (1998), Hướng dẫn thực hành tính toán trên chương trình MAPLE V, NXB Giáo dục, Hà Nội. TẠP CHÍ KHOA HỌC VÀ CÔNG NGHỆ, ĐẠI HỌC ĐÀ NẴNG - SỐ 5(28).2008 68 [3] Lê Ngọc Lăng, Tống Đình Quỳ, Ng[r]

(t) is continuous on [α, β], too. Then, by a similarmethod to the proof of (2.3) together with Lemma 2.2, we can obtain (2.4) immediately.For the other ordinary cases, i.e., a = 0, we only need to move the interval [α, β] evenlysuch that this interval symmetrizes about the origin. Then, simi[r]

Hindawi Publishing CorporationAdvances in Difference EquationsVolume 2011, Article ID 513757, 14 pagesdoi:10.1155/2011/513757Research ArticleOscillation Criteria forSecond-Order Neutral Delay Dynamic Equationswith Mixed NonlinearitiesEthiraju Thandapani,1Veeraraghavan Piramanantham,2and[r]

, then there exists a homomorphism H : G1→G2with d(h(x),H(x)) &lt;δfor all x∈ G1?In the following year, Hyers [2] partially solved the Ulam problem for the case whereG1and G2are Banach spaces. Furthermore, the result of Hyers has been generalized byRassias (see [3]). Since then, the stabi[r]

AcknowledgmentsThe authors are very grateful to the referees for careful reading of the original manu-script and for valuable suggestions on improving this paper. This project is supported bythe Natural Science Foundation of Jiangsu Education Office (06KJB110010) and Jiang[r]

sl´yandˇReh´ak and some results ofˇReh´ak for half-linear equations on time scales. Several ex-amples are considered to illustrate the main results.Copyright © 2006 L. Erbe et al. This is an open access article distributed under the Cre-ative Commons Attribution License,[r]

2. Taylor Modets for Derivations and Antiderivations
In the spirit of the idea of embedding the elementary operations of addition, mul- tiplication, and differentiation and their Inverses that are defined on the class of<[r]

Xem Thêm " TAYLOR MODEL "

Xem Thêm " DIFFERENTIAL EQUATION OF FIRST ORDER AND HIGHER DEGREE PDF "

6.2.3. Theorems about Differentiable Functions. L’Hospital Rule . . . . . . . . . . . . . . . . . 2546.2.4. Higher-Order Derivatives and Differentials. Taylor’s Formula . . . . . . . . . . . . . . . 2556.2.5. Extremal Points. Points of Inflection 2576.2.6. Qualitative Anal[r]