bài 17 nhà nước cộng hòa xã hội chủ nghĩa việt nam tt
ONE PARAMETER FAMILY OF LINEAR DIFFERENCE EQUATIONS AND THE STABILITY PROBLEM FOR THE NUMERICAL pdf
... with respect to the continuous initial value problem, it is not necessary to approximate the latter with a discrete problem of the same type In the case of first order differential equation, for ... limitations on the choice of the methods in the class of LMMs used as initial value methods (IVMs) As matter of fact, there are not methods with order greater than two having the critical point asymptotically ... terminology used in Numerical Analysis is often different from the one used in the Difference Equations setting In order to avoid confusion, it is worth to note that the terms such as “stable methods” refer...
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báo cáo hóa học:" Research Article Existence of Positive Solutions of Nonlinear Second-Order Periodic Boundary Value Problems" ppt
... the fact that μ0 ≤ μ0 γ 1 μ0 Γ ≤ μ0 , 3.21 though μ0 Γ is a little bit smaller than 1, the existence of positive solutions of 3 .17 will not be guaranteed in this case Proof of Theorem 3.2 We ... and v of 1.13 and 1.14 , should be corrected to the form ⎧ ⎪v t u s , ≤ s ≤ t ≤ T, α u s v s ⎨ 1 .17 G t, s u t v t − v v ⎪ ⎩v s u t , ≤ t ≤ s ≤ T This will be done in Section Finally in Section ... 2.3 Let a ∈ Λ ∪ Λ− Then the Green’s function G t, s induced by u and v is explicitly given by 1 .17 , that is, G t, s us v s v v −u T u t v t ⎧ ⎨v t u s , − v ⎩v s u t , ≤ s ≤ t ≤ T, ≤ t ≤ s ≤...
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báo cáo hóa học:" Nodal solutions of second-order two-point boundary value problems" potx
... u(0) = u(1) = 0} with the norm u E = max |u| + max |u | t∈[0,1] t∈[0,1] Define L : D(L) → Y by setting Lu := −u (t), t ∈ [0, 1], u ∈ D(L), where D(L) = {u ∈ C [0, 1] | u(0) = u(1) = 0} Then L−1 ... two-point boundary value problems with nonlinearities across several eigenvalues J Appl Math Lett 18, 587–595 (2005) [4] Rabinowitz, PH: Some global results for nonlinear eigenvalue problems ... Spectrum of one dimensionalp-Laplacian with indefinite weight Electron J Qual Theory Diff Equ 2002 (17) , 11 pp (2002) [12] Dai, G, Ma, R: Unilateral global bifurcation and radial nodal solutions for...
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Báo cáo hóa học: " Research Article Multiplicity of Positive Periodic Solutions of Singular Semipositone Third-Order Boundary Value Problems" doc
... Furthermore, unk satisfies the integral equation 2π unk t − ω ds G t, s F s, J unk s nk 3.12 Letting k → ∞, we obtain that 2π ut G t, s F s, J u s − ω ds, 3.13 where the uniform continuity of ... we have Fn t, J un t −ω F t, J un t ≥ g0 J un t − ω ≥ ρ2 J un t − ω > ρ2 r ρH −ω g0 J un t −ω 3 .17 Yigang Sun and if un t − L/ρ2 ≤ 1/n, we have nρ −ω F t, By 3.16 and integrating 3.2 with λ Fn ... Applications J Chu, P J Torres, and M Zhang, “Periodic solutions of second order non-autonomous singular dynamical systems,” Journal of Differential Equations, vol 239, no 1, pp 196–212, 2007 M A del Pino...
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CONSTRUCTION OF UPPER AND LOWER SOLUTIONS FOR SINGULAR DISCRETE INITIAL AND BOUNDARY VALUE PROBLEMS potx
... (2.16) k=k0 Now since ∆u(k0 − 1) ≥ 0, we have j −∆u( j) = ϕ−1 h(M) ϕ−1 p p q(k) for j ≥ k0 (2 .17) k=k0 We sum the above from k0 to T to obtain u k0 − u(T + 1) ≤ ϕ−1 h(M) p T j =k0 j ϕ−1 p q(k) ... on singular nonlinear boundary value problems for the oneu dimensional p-Laplacian, Appl Math Lett 14 (2001), no 2, 189–194 214 [10] [11] Discrete initial and boundary value problems R Man´ sevich...
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báo cáo hóa học:" Research Article Exponential Stability and Estimation of Solutions of Linear Differential Systems of Neutral Type with Constant Coefficients" pot
... H 2.20 −β t−s T T x s G2 x s ds ˙ ˙ x s G1 x s t−τ We use this expression in 2 .17 Since λmin S > 0, we obtain omitting terms x t − τ x t−τ ˙ and d V0 x t , t ≤ λmin S dt × − −β λmax H t V0 x ... t , t ˙ ˙ λmax H x t 2.25 t−τ We substitute this expression into inequality 2 .17 Since λmin S > 0, we obtain omitting ˙ terms x t − τ and x t − τ d V0 x t , t ≤ −λmin S x t dt β −V0 x t , t ... − τ 2.14 Boundary Value Problems Now it is easy to verify that the last expression can be rewritten as d V0 x t , t dt − xT t , xT t − τ , xT t − τ ˙ ⎛ ⎜ ×⎜ ⎝ −AT H − HA − G1 − AT G2 A −HB −...
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Báo cáo hóa học: "Research Article Existence and Uniqueness of Solutions for Higher-Order Three-Point Boundary Value Problems" ppt
... Grace, and D O’Regan, “Semipositone higher-order differential equations,” Applied Mathematics Letters, vol 17, no 2, pp 201–207, 2004 A Cabada, “The method of lower and upper solutions for second, ... − g w0 a, x a , , wn−2 a, x n−2 a , x n−1 a ≤ λ β n−2 a − g β a , , β n−2 a , Case t1 , 3 .17 < Mn−2 c In this case, max x n−2 t : x n−2 c ≥ Mn−2 > , 3.18 t∈ a,c and x n−1 c ≥ For λ 0, ... and S Liu, “Solvability of a third-order two-point boundary value problem,” Applied Mathematics Letters, vol 18, no 9, pp 1034–1040, 2005 M R Grossinho and F M Minhos, “Existence result for some...
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Báo cáo hóa học: "Research Article Asymptotic Representation of the Solutions of Linear Volterra Difference Equations" pdf
... vol 36, no 2, pp 89–111, 1990 17 V Kolmanovskii and L Shaikhet, “Some conditions for boundedness of solutions of difference Volterra equations,” Applied Mathematics Letters, vol 16, no 6, pp 857–862, ... then the constant A satisfies either ∞ A > μ1 − − K i μ−i 3.16 i or A < −μ1 − − ∞ −1 i K i μ−i , 3 .17 i iii if G r < 1, then the constant A satisfies either ∞ A≥r−1− K i r −i 3.18 i or ∞ A ≤ −r − ... and K ≥ 0, then μ1 A/ l|K l | 4.16 K , moreover 4.14 and 4.15 are equivalent to − K −1 K −1 K 4 .17 Example 4.4 Let q ∈ R \ {0} and K i : qi , i ∈ Z Then, 3.7 has the following form: n Δx n Ax...
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Báo cáo hóa học: "EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR SOME THREE-POINT NONLINEAR BOUNDARY VALUE PROBLEMS" pptx
... continuous on QλM , then there exists δ > such that λ Fx − Fx0 ≤ τ0 (3 .17) for any x ∈ QλM with x − x0 < δ By (3.16) and (3 .17) , we have Tλ x (t) ≤ Tλ x0 (t) + τ0 τ LλM z0 (t) ≤ u∗ (t) − LλM z0 ... we have Lτ (η) ≥ q1,τ (η) p0,τ (η) , q1,τ (0) + q1,τ (η) p0,τ (1) + p0,τ (η) Lτ x (2.22) By (2 .17) and (2.22), we have (Lτ x)(t) ≥ θτ Lτ x t (2.23) This implies that Lτ : P → Qτ Now we will ... p0,τ (η) p0,τ (1) − γ p0,τ (η) q1,τ (s) a(s)x(s)ds q1,τ (0) η p0,τ (1) p0,τ (1) − γ p0,τ (η) ≥ (2 .17) η p0,τ (η) q1,τ (s) a(s)x(s)ds q1,τ (0) η q1,τ (s)a(s)x(s)ds (2.19) X Xian and D O’Regan By...
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Báo cáo hóa học: "REPRESENTATION OF SOLUTIONS OF LINEAR DISCRETE SYSTEMS WITH CONSTANT COEFFICIENTS AND PURE DELAY" ppt
... F(k,n) := F(k + 1,n) − F(k,n) (3 .17) is said to be a partial difference operator, provided that the right-hand side exists In the following formula (which proof is omitted) we suppose that all used ... it by the method of steps, we conclude that the solution of the problem (2.1), (2.2) can be written in the form ⎧ ⎪1 if k ∈ Z0 , ⎪ − ⎪ ⎪ ⎪ ⎪ ⎪ k ⎪ ⎪1 + b · if k ∈ Z4 , ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ k k−3 ... 1)m ! B j −1 ( j − 1)! k − ( j − 1)m − ( j − 1) ! j =1 B j −1 · =B I+ j =2 k − ( j − 1)m j −1 (2 .17) Now we change the index of summation j by j + Then ΔeBk = B I + m −1 Bj · j =1 k − jm j (2.18)...
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Báo cáo hóa học: "Research Article Periodic and Almost Periodic Solutions of Functional Difference Equations with Finite Delay" pdf
... references therein) Recently, several papers [12 17] are devoted to study almost periodic solutions of difference equations To the best of our knowledge, little work has been done on almost periodic ... system of difference equations,” Computers & Mathematics with Applications, vol 50, no 10–12, pp 172 5 175 4, 2005 [13] Y Hamaya, “Existence of an almost periodic solution in a difference equation with ... (2.6) Periodic systems In this section, we discuss the existence of periodic solutions of (2.6), namely, x(n + 1) = F n,xn , n ≥ 0, (3.1) under a periodic condition (H3) as follows (H3) The F(n,...
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Báo cáo hóa học: "SECOND-ORDER ESTIMATES FOR BOUNDARY BLOWUP SOLUTIONS OF SPECIAL ELLIPTIC EQUATIONS CLAUDIA ANEDDA, ANNA BUTTU, AND GIOVANNI " pot
... de l’Hˆ pital’s rule Using (2.11), (2.10) can be rewritten o as 2F(s) 1/2 f (s) −1 ∞ = 2F(t) s −1/2 dt + O(1)s−β ∞ s 2F(t) −1/2 dt (2.13) Putting s = Φ(δ) and using the equation −Φ (δ) = (2F(Φ(δ)))1/2 ... 2F(s) −1/2 dt −1/2 = (3.9) Using (3.9), (3.8) can be rewritten as 2F(s) 1/2 f (s) −1 = ∞ s 2F(t) −1/2 dt + O(1)e−s ∞ s 2F(t) −1/2 dt (3.10) Putting s = Ψ(δ) and recalling that −Ψ (δ) = (2F(Ψ(δ)))1/2 ... E-mail address: canedda@unica.it Anna Buttu: Dipartimento di Matematica, Universit´ di Cagliari, Via Ospedale 72, a 09124 Cagliari, Italy E-mail address: buttu@uncia.it Giovanni Porru: Dipartimento...
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ON THE SOLVABILITY OF INITIAL-VALUE PROBLEMS FOR NONLINEAR IMPLICIT DIFFERENCE EQUATIONS PHAM KY ANH pdf
... -component of x0 Further, putting n = in (2.8) and noting that V−1 = V0 , u0 = P−1 x0 = P0 x0 , we find that a consistent initial value x0 must satisfy a “hidden” constraint, namely, Q0 (I + G−1 B0 ... Mathematics, Mechanics, and Informatics, College of Science, Vietnam National University, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam E-mail address: anhpk@vnu.edu.vn Ha Thi Ngoc Yen: Department ... multipoint boundary-value problems for linear implicit nonautonomous systems of difference equations, Vietnam J Math 29 (2001), no 3, 281–286 M S Berger, Nonlinearity and Functional Analysis, Lectures on...
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NONOSCILLATORY HALF-LINEAR DIFFERENCE EQUATIONS AND RECESSIVE SOLUTIONS ˇ ´ MARIELLA CECCHI, pdf
... vn+1 or ∆vn + wn vn+1 ≥ Since wn ≥ and ∞ n=N wn < ∞, we have < ∞ −1 j =N (1 + w j ) (2.10) < ∞ Putting ∞ hn = , + wj j =n (2.11) we have hn > and ∆hn = hn wn Multiplying (2.10) by hn , we obtain ... bk Φ xk+1 − Φ zk+1 ≤H k=n ∞ ≤ HM bk Ak+1 k=n p−2 ∞ Φ∗ a j j =k+1 Φ∗ z[1] − Φ∗ x[1] j j (3.15) Putting un = sup [1] [1] Φ∗ xk − Φ∗ zk :k≥n , (3.16) 200 Recessive solutions for half-linear equations ... un ≤ HM bk Ak+1 p−2 k=n ∞ ≤ HM bk uk+1 Ak+1 ∞ uj Φ∗ a j j =k+1 p−2 k=n ∞ = HM ∞ Φ∗ a j j =k+1 (3 .17) bk Φ Ak+1 uk+1 k=n Taking into account (1.10), we can apply Lemma 2.3 and we obtain un ≡ for...
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Tài liệu Solution of Linear Algebraic Equations part 1 docx
... Equation (2.0.1) can be written in matrix form as A·x=b (2.0.2) Here the raised dot denotes matrix multiplication, A is the matrix of coefficients, and b is the right-hand side written as a column vector, ... any servercomputer, is strictly prohibited To order Numerical Recipes books,diskettes, or CDROMs visit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk ... any servercomputer, is strictly prohibited To order Numerical Recipes books,diskettes, or CDROMs visit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk...
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Tài liệu Solution of Linear Algebraic Equations part 2 ppt
... any servercomputer, is strictly prohibited To order Numerical Recipes books,diskettes, or CDROMs visit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk ... any servercomputer, is strictly prohibited To order Numerical Recipes books,diskettes, or CDROMs visit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk ... any servercomputer, is strictly prohibited To order Numerical Recipes books,diskettes, or CDROMs visit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk...
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Tài liệu Solution of Linear Algebraic Equations part 11 ppt
... any servercomputer, is strictly prohibited To order Numerical Recipes books,diskettes, or CDROMs visit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk ... any servercomputer, is strictly prohibited To order Numerical Recipes books,diskettes, or CDROMs visit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk ... any servercomputer, is strictly prohibited To order Numerical Recipes books,diskettes, or CDROMs visit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk...
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Tài liệu Solution of Linear Algebraic Equations part 3 pdf
... any servercomputer, is strictly prohibited To order Numerical Recipes books,diskettes, or CDROMs visit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk ... any servercomputer, is strictly prohibited To order Numerical Recipes books,diskettes, or CDROMs visit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk ... Backsubstitution But how we solve for the x’s? The last x (x4 in this example) is already isolated, namely x4 = b4 /a44 (2.2.2) x3 = [b − x4 a34 ] a33 and then proceed with the x before that one The...
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Tài liệu Solution of Linear Algebraic Equations part 4 docx
... for βij , namely i−1 βij = aij − αik βkj (2.3.12) k=1 (When i = in 2.3.12 the summation term is taken to mean zero.) Second, for i = j + 1, j + 2, , N use (2.3.10) to solve for αij , namely ... any servercomputer, is strictly prohibited To order Numerical Recipes books,diskettes, or CDROMs visit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk ... any servercomputer, is strictly prohibited To order Numerical Recipes books,diskettes, or CDROMs visit website http://www.nr.com or call 1-800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk...
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