solutions of linear nonhomogeneous equations and initial value problems

Ngày tải lên: 31/03/2014, 15:56

... number of initial conditions should be equal to the number of roots of the characteristic polynomial inside the unit circle and, of course, the number of conditions at the end of the interval of ... if the number of initial conditions is equal to the number of roots of the characteristic polynomial inside the unit circle and the number of conditions at the end of the interval of integration ... k −2 This completes the proof Lemma 3.5 The solutions ρk (z) and σk (z) of (3.4) are linearly independent (3.14) 10 Difference equations and the stability problem Proof Let us consider the Casorati...

Ngày tải lên: 23/06/2014, 00:20

... Boundary Value Problems Finally, we state a result concerning the global structure of the set of positive solutions of parameterized nonlinear operator equations, which is essentially a consequence of ... Green’s function G t, s of 1.1 , 1.2 Let u be the unique solution of the initial value problem u a tu 0, u0 0, u 1, 1.13 −1 1.14 and let v be the unique solution of the initial value problem v at ... study the existence of one-sign solutions of the nonlinear problem x f t, x , t ∈ 0, T , 1.18 x x T , x x T The proofs of the main results are based on the properties of G and the Dancer’s global...

Ngày tải lên: 21/06/2014, 11:20

... study the existence and multiplicity of nodal solutions of the nonlinear second-order two-point boundary value problems, u + f (t, u) = 0, t ∈ (0, 1), u(0) = u(1) = The proof of our main results ... completely continuous linear operator, and is not an eigenvalue of T , then ind(I − T, θ) = (−1)β , where β is the sum of the algebraic multiplicities of the eigenvalues of T large than 1, and β = if T ... to Lemma 2.3 Proof of main results Proof of Theorems 1.1 and 1.2 We only prove Theorem 1.1 since the proof of Theorem 1.2 is similar ν It is clear that any solution of (2.4) of the form (1, u)...

Ngày tải lên: 21/06/2014, 17:20

... to superlinear repulsive singular equations, ” Journal of Differential Equations, vol 211, no 2, pp 282–302, 2005 A C Lazer and S Solimini, “On periodic solutions of nonlinear differential equations ... method of lower and upper solutions or second, third, fourth and higher order boundary value problem,” Applied Mathematics and Computation, vol 40, pp 135–145, 1990 10 J Chu and Z Zhou, “Positive solutions ... Chu and M Li, “Positive periodic solutions of Hill’s equations with singular nonlinear perturbations,” to appear in Nonlinear Analysis: Theory, Methods & Applications J Chu, P J Torres, and M...

Ngày tải lên: 22/06/2014, 00:20

... O’Regan, V Lakshmikantham, and S Leela, Existence of positive solutions for singular initial and boundary value problems via the classical upper and lower solution approach, Nonlinear Anal 50 (2002), ... boundary value problems, Nonlinear Anal 39 (2000), no 2, 207–215 R P Agarwal, D O’Regan, and V Lakshmikantham, Existence criteria for singular initial value problems with sign changing nonlinearities, ... D O’Regan, and P J Y Wong, Positive Solutions of Differential, Difference and Integral Equations, Kluwer Academic Publishers, Dordrecht, 1999 P Habets and F Zanolin, Upper and lower solutions for...

Ngày tải lên: 23/06/2014, 00:20

... functionals 1.9 and 1.10 have not yet been applied as suggested to the study of stability and estimates of solutions of 1.1 Exponential Stability and Estimates of the Convergence of Solutions to ... metric C1 Estimates of Solutions in a General Case Now we will estimate the norms of solutions of 1.1 and the norms of their derivatives in the case of the assumptions of Theorem 2.5 or Theorem ... the derivative ˙ of the initial function on the initial interval −τ, Now we give a statement on the stability of the zero solution of system 1.1 and estimates of the convergence of the solution,...

Ngày tải lên: 21/06/2014, 11:20

... of solutions for a class of third-order nonlinear boundary value problems, ” Journal of Mathematical Analysis and Applications, vol 294, no 1, pp 104–112, 2004 Y Feng and S Liu, “Solvability of ... boundary value problems, ” Journal of Mathematical Analysis and Applications, vol 167, no 1, pp 43–48, 1992 17 M Pei and S K Chang, “Existence and uniqueness of solutions for third-order nonlinear ... boundary value problems, ” Journal of Mathematical Analysis and Applications, vol 327, no 1, pp 23–35, 2007 18 Y Shi and M Pei, “Two-point and three-point boundary value problems for nth-order nonlinear...

Ngày tải lên: 21/06/2014, 20:20

... “Asymptotic solutions and error estimates for linear systems of difference and differential equations, ” Journal of Mathematical Analysis and Applications, vol 290, no 1, pp 343– 362, 2004 11 S Bodine and ... of solutions of difference Volterra equations, ” Applied Mathematics Letters, vol 16, no 6, pp 857–862, 2003 18 Z H Li, “The asymptotic estimates of solutions of difference equations, ” Journal of ... A D Applelby, I Gy˝ ri, and D W Reynolds, “On exact convergence rates for solutions of linear o systems of Volterra difference equations, ” Journal of Difference Equations and Applications, vol 12,...

Ngày tải lên: 22/06/2014, 11:20

... Ma and N Castaneda, Existence of solutions of nonlinear m-point boundary -value problems, Journal of Mathematical Analysis and Applications 256 (2001), no 2, 556–567 [8] J R L Webb, Positive solutions ... boundary value problems if the nonlinearity f is either superlinear or sublinear The purpose of this paper is to X Xian and D O’Regan extend the main results of [1, 2, 5, 9] to the nonlinear three-point ... 2, 467–480 [4] C P Gupta and S I Trofimchuk, Existence of a solution of a three-point boundary value problem and the spectral radius of a related linear operator, Nonlinear Analysis Theory, Methods...

Ngày tải lên: 22/06/2014, 22:20

... theory of linear equations, as the sum of the solution of adjoint homogeneous problem (3.1), (3.2) (satisfying the same initial data) and a particular solution of (3.15) being zero on initial ... investigation of such asymptotic problems as describing the asymptotic behavior of solutions and the investigation concerning boundedness, convergence, or stability of solutions With the aid of different ... of a matrix relative to discrete delayed equations and give an J Dibl´k and D Y Khusainov ı analogue of formula (1.6) for homogeneous and nonhomogeneous problems (1.1), (1.2) with pure delay Discrete...

Ngày tải lên: 22/06/2014, 22:20

... Baker and Y Song, “Periodic solutions of discrete Volterra equations, ” Mathematics and Computers in Simulation, vol 64, no 5, pp 521–542, 2004 [4] C Cuevas and M Pinto, “Asymptotic properties of solutions ... 174–194, 2006 [16] Y Song and H Tian, “Periodic and almost periodic solutions of nonlinear Volterra difference equations with unbounded delay,” to appear in Journal of Computational and Applied Mathematics ... periodic solutions of an almost periodic system,” Funkcialaj Ekvacioj, vol 12, pp 23–40, 1969 [2] R P Agarwal, Difference Equations and Inequalities, vol 228 of Monographs and Textbooks in Pure and...

Ngày tải lên: 22/06/2014, 22:20

... behaviour of large solutions of semilinear elliptic [7] problems, Differential and Integral Equations 11 (1998), no 1, 23–34 , Dependence of blowup rate of large solutions of semilinear elliptic equations, ... blow-up solutions of elliptic equations, to appear in Differential Integral Equations [4] C Bandle, Asymptotic behaviour of large solutions of quasilinear elliptic problems, Zeitschrift f¨ r u Angewandte ... Asymptotic estimates and convexity of large solutions to semilinear elliptic equations, Differential and Integral Equations 10 (1997), no 2, 219–229 [14] J B Keller, On solutions of Δu = f (u), Communications...

Ngày tải lên: 22/06/2014, 22:20

... Anh and L C Loi, On 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 ... Nonlinear Problems in Mathematical Analysis Pure and Applied Mathematics, Academic Press, New York, 1977 L C Loi, N H Du, and P K Anh, On linear implicit non-autonomous systems of difference equations, ... rz, On linear differential-algebraic equations and linearizations, Appl Numer Math 18 a (1995), no 1–3, 267–292 Pham Ky Anh: Department of Mathematics, Mechanics, and Informatics, College of Science,...

Ngày tải lên: 23/06/2014, 00:20

... for half -linear differsa ence equations, J Differ Equations Appl 10 (2004), no 9, 797–808 , Half -linear equations and characteristic properties of the principal solution, J Differential Equations ... Differential, Difference and Integral Equations, Kluwer Academic Publishers, Dordrecht, 2001 C D Ahlbrandt, Dominant and recessive solutions of symmetric three term recurrences, J Differential Equations 107 ... Doˇl´ , and M Marini, Summation characterization of the recessive solusa sy tion for half -linear equations, in preparation M Cecchi, Z Doˇl´ , and M Marini, On recessive and dominant solutions...

Ngày tải lên: 23/06/2014, 00:20

... Much of the sophistication of complicated linear equation-solving packages” is devoted to the detection and/ or correction of these two pathologies As you work with large linear sets of equations, ... Solution of Linear Algebraic Equations Coleman, T.F., and Van Loan, C 1988, Handbook for Matrix Computations (Philadelphia: S.I.A.M.) Forsythe, G.E., and Moler, C.B 1967, Computer Solution of Linear ... out equations only for the case of four equations and four unknowns, and with three different righthand side vectors that are known in advance You can write bigger matrices and extend the equations...

Ngày tải lên: 15/12/2013, 04:15

... row in A by a linear combination of itself and any other row, as long as we the same linear combination of the rows of the b’s and (which then is no longer the identity matrix, of course) • Interchanging ... Reduction and Error Analysis for the Physical Sciences (New York: McGraw-Hill), Program B-2, p 298 Westlake, J.R 1968, A Handbook of Numerical Matrix Inversion and Solution of Linear Equations ... 4) of the vector solution of the jth right-hand side (j = 1, 2, 3), the one whose coefficients are bij , i = 1, 2, 3, 4; and that the matrix of unknown coefficients yij is the inverse matrix of...

Ngày tải lên: 15/12/2013, 04:15

... the set of n linear equations A · x = b a[1 n][1 n], c[1 n], and d[1 n] are input as the output of the routine qrdcmp and are not modified b[1 n] is input as the right-hand side vector, and is ... b[]) Solves the set of n linear equations R · x = b, where R is an upper triangular matrix stored in a and d a[1 n][1 n] and d[1 n] are input as the output of the routine qrdcmp and are not modified ... i,j,k; 102 Chapter Solution of Linear Algebraic Equations We will make use of QR decomposition, and its updating, in §9.7 CITED REFERENCES AND FURTHER READING: Golub, G.H., and Van Loan, C.F 1989,...

Ngày tải lên: 15/12/2013, 04:15

... Westlake, J.R 1968, A Handbook of Numerical Matrix Inversion and Solution of Linear Equations (New York: Wiley) Suppose we are able to write the matrix A as a product of two matrices, L·U=A (2.3.1) ... is reduced, and the increasing numbers of predictable zeros reduce the count to one-third), and N M times, respectively Each backsubstitution of a right-hand side is N executions of a similar ... backsubstitution The combination of Gaussian elimination and backsubstitution yields a solution to the set of equations The advantage of Gaussian elimination and backsubstitution over Gauss-Jordan...

Ngày tải lên: 24/12/2013, 12:16

... the loop of the above fragment and (e.g.) divide by powers of ten, to keep track of the scale separately, or (e.g.) accumulate the sum of logarithms of the absolute values of the factors and the ... Prentice-Hall), Chapters 9, 16, and 18 Westlake, J.R 1968, A Handbook of Numerical Matrix Inversion and Solution of Linear Equations (New York: Wiley) Stoer, J., and Bulirsch, R 1980, Introduction ... (Cambridge: Cambridge University Press) 2.4 Tridiagonal and Band Diagonal Systems of Equations The special case of a system of linear equations that is tridiagonal, that is, has nonzero elements...

Ngày tải lên: 24/12/2013, 12:16