second order partial differential equation pdf

... nonlinear second- order singular and impulsive differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol 69, no 11, pp 3774–3789, 2008 Y Dong, “Periodic solutions for second order ... of the result for problem P with two-point boundary condition Let us consider the following second- order impulsive differential systems u t λh1 t f u t , v t 0, t ∈ 0, , t / t1 , v t μh2 t g u ... 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 bounded above Proof Suppose on the contrary...

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... The Partial Differential Equation (PDE) Toolbox provides a powerful and flexible environment for the study and solution of partial differential equations in two space dimensions and time The equations ... Analogously, we shall use the terms parabolic equation and hyperbolic equation for equations with spatial operators like the one above, and first and second order time derivatives, respectively Ω is ... error reports Subscribing user registration Order status, license renewals, passcodes Sales, pricing, and general information Partial Differential Equation Toolbox User’s Guide © COPYRIGHT 1984...

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... constants Equation 1.3 is termed a first -order, linear, ordinary differential equation with variable coefficients These terms are explained below Term Explanation Differential equation Ordinary First -order ... characteristic equation for Equation 1.9 (note that it is a scalar equation) The values of λ that satisfy Equation 1.10 are the eigenvalues of Equation 1.9 For the 2x2 problem of Equations 1.8, Equation ... which implements the Euler method of Equation 1.28, the modified Euler method of Equations 1.30, the secondorder RK of Equations 1.42, and the third -order RK of Equations 1.44 Copyright by Chapman...

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... Periodic solutions of nonlinear second order difference equations Adv Differ Equ 2005, 173–192 (2005) Tang, XH, Lin, XY, Xiao, L: Homoclinic solutions for a class of second order discrete Hamiltonian ... solutions of subquadratic second order difference equations J London Math Soc 68, 419–430 (2003) 18 Kocic, VL, Ladas, G: Global Behavior of Nonlinear Difference Equations of Higher Order with Applications ... Difference Equations 2011, 2011:57 http://www.advancesindifferenceequations.com/content/2011/1/57 Page of 16 It is clear that system (1.1) is a discretization of the following second differential...

Ngày tải lên: 20/06/2014, 22:20

... Dongsheng et al Advances in Difference Equations 2011, 2011:46 http://www.advancesindifferenceequations.com/content/2011/1/46 Page of Second, one investigates (b) From Equation (1.1), one has − xk xn−1 ... a fourth order rational difference equation J Math Anal Appl 311(1), 103–111 (2005) doi:10.1016/j.jmaa.2005.02.063 Xi, H, Sun, T: Global behavior of a higher -order rational difference equation ... doi:10.1186/1687-1847-2011-46 Cite this article as: Dongsheng et al.: On a class of second- order nonlinear difference equation Advances in Difference Equations 2011 2011:46 Page of ...

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... variational methods when we solve superlinear differential equations such as elliptic problems, Dirac equations, Hamiltonian systems, wave equations, and Schrödinger equations Theorem 3.2 Assume that F(t, ... solutions for p(x)-Laplacian equations in ℝN Nonlinear Anal 59, 173–188 (2004) 19 Rabinowitz, PH: Minimax methods in critical point theory with applications to differential equations In CBMS Reg Conf ... doi:10.1186/1687-2770-2011-33 Cite this article as: Zhang et al.: Infinitely many periodic solutions for some second- order differential systems with p(t)-Laplacian Boundary Value Problems 2011 2011:33 Submit your...

Ngày tải lên: 20/06/2014, 22:20

... solutions for non-autonomous second order systems J Math Anal Appl 202, 465–469 (1996) doi:10.1006/jmaa.1996.0327 Tang, CL: Periodic solutions for nonautonomous second order systems with sublinear ... Solutions of a second- order Hamiltonian with periodic boundary conditions Comm Pure Appl Anal 9, 1053–1067 (2010) 14 Wang, Z, Zhang, J: Periodic solutions of non-autonomous second order Hamiltonian ... class of non-autonomous second- order systems with linear nonlinearity Nonlinear Anal 60, 325–335 (2005) 12 Wang, Z, Zhang, J: Periodic solutions of a class of second order non-autonomous Hamiltonian...

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... Comparison theorems for infinite systems of differential functional equations and strongly coupled infinite systems of first order partial differential equations Rocky Mt J Math 10, 237–246 (1980) ... first order partial differential functional equations Nonlinear Anal TMA 14, 837–850 (1990) doi:10.1016/0362-546X(90)90024-B 14 Topolski, K: On the uniqueness of viscosity solutions for first order ... order partial differential functional equations Ann Polon Math 98, 39–61 (2010) doi:10.4064/ap98-1-3 doi:10.1186/1029-242X-2011-15 Cite this article as: Kamont: Weak solutions of functional differential...

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... problems for differential- operator equations Nauk Dumka, Kiev, 284 (1984) (Russian) 31 Yakubov, S, Yakubov, Ya: Differential- Operator Equations Ordinary and Partial Differential Equations Chapman ... simple identity for eigenvalue of second order differential operator DAN SSSR 88(4), 593–596 (1953) 19 Aslanova, NM: Trace formula for Sturm-Liouville operator equation Proc Math Mech Natl Acad ... Sturm-Liouville operator equation Ukr Math J 32(2), 248–252 (1980) Aliev, BA: Asymptotic behavior of eigenvalue of one boundary value problem for elliptic dif.-operat equation of second order Ukr Math...

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... measurements of second- order optical nonlinearities in asymmetrical quantum dots with the aim of to detect the magnitude of this effect Abbreviations OR: optical rectification; SHG: second harmonic ... when L a∗, or equivalently hω0 R∗, and the weak¯ ∗ a0, or hω0 confinement limit when L R∗ ¯ The second- order nonlinear optical coefficients can be obtained by density matrix approach and perturbation ... the modification of the dipole matrix elements defined in Equations14, 15, and 20 when the Coulomb interaction is considered According to Equation 18, the peak intensity of OR coefficient depends...

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... singular boundary value problem of third -order differential equations,” Mathematica Slovaca, vol 60, no 4, pp 485–494, 2010 Y Sun, “Positive solutions for third -order three-point nonhomogeneous boundary ... grateful to the referees for valuable suggestions and comments References M Gregus, “Third order linear Differential equations,” in Mathematics and Its Applications, Reidel, Dordrecht, the Netherlands, ... and y ≤ τ x , z ≤τ x Boundary Value Problems 3 Singular Third -Order Boundary Value Problem This section discusses singular third -order boundary value problem 1.1 Let P {x ∈ C I | x t ≥ 0, ∀...

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... Difference Equations Differential equations with a small parameter < ε multiplying the highest order derivatives are called singularly perturbed differential equations Typically, the solutions of such equations ... 1, pp 73–97, 1999 21 R E O’Malley Jr., “Two-parameter singular perturbation problems for second- order equations,” Journal of Mathematics and Mechanics, vol 16, pp 1143–1164, 1967 22 A A Samarskii, ... xN0 , − xN0 N − 1, , 2, Qi,N0 βi , Advances in Difference Equations 11 N N Table 1: Approximate errors eε and eN and the computed orders of convergence pε on the piecewise uniform mesh ωN for...

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... for a second order nonlinear neutral delay difference equation, ” Computers & Mathematics with Applications, vol 57, no 4, pp 587–595, 2009 Q Meng and J Yan, “Bounded oscillation for second- order ... solution of a second- order linear neutral difference equation, ” Applied Mathematics Letters, vol 20, no 8, pp 892–899, 2007 I Gy˝ ri and G Ladas, Oscillation Theory of Delay Differential Equations, ... properties of solutions of second- order neutral difference equations,” Nonlinear Analysis: Theory, Methods & Applications, vol 63, no 5–7, pp e789–e799, 2005 14 Advances in Difference Equations 11 E Thandapani,...

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