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Asymptotic Properties of Solutions of Fourth-Order Delay Differential Equations
Symmetry, 2019 In the paper, we study the oscillation of fourth-order delay differential equations, the present authors used a Riccati transformation and the comparison technique for the fourth order delay differential equation, and that was compared with the ...
Sandra Pinelas +2 more
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Nonlinear Oscillation of Fourth Order Differential Equations
Canadian Journal of Mathematics, 1976In this paper we are concerned with the fourth order nonlinear differential equation where the following conditions are always assumed to hold: (a) r(t ...
Kusano, Takasi, Naito, Manabu
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Fourth-Order Differential Equations on Geometric Graphs
Journal of Mathematical Sciences, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Borovskikh, A. V., Lazarev, K. P.
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Asymptotic Solutions of a Fourth Order Differential Equation
Studies in Applied Mathematics, 2007In this paper, we derive uniform asymptotic expansions of solutions to the fourth order differential equation image where x is a real variable and λ is a large positive parameter. The solutions of this differential equation can be expressed in the form of contour integrals, and uniform asymptotic expansions are derived by using the cubic ...
Wong, R., Zhang, H. Y.
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Fourth Order Differential Equations
2004In addition to discussing general fourth order nonlinear equations with quasiderivatives, we consider sublinear equations in self-adjoint form, a two term nonlinear equation, and then fourth order linear equations.
Miroslav Bartušek +2 more
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The Sinc-Galerkin Method for Fourth-Order Differential Equations
SIAM Journal on Numerical Analysis, 1991The Sinc-Galerkin method originally proposed by Stenger is extended to handle fourth-order ordinary differential equations. The exponential convergence rate of the method, $O(e^{ - \kappa \sqrt M } )$ is carefully developed and the special features of the discrete system are described. Spectral properties and conditioning of the associated matrices are
Ralph Conover Smith, John Lund
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The generalized differential quadrature rule for fourth‐order differential equations
International Journal for Numerical Methods in Engineering, 2001AbstractThe generalized differential quadrature rule (GDQR) proposed here is aimed at solving high‐order differential equations. The improved approach is completely exempted from the use of the existing δ‐point technique by applying multiple conditions in a rigorous manner.
Wu, T.Y., Liu, G.R.
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On the stability of a nonhomogeneous vector differential equation of the fourth-order
Applied Mathematics and Computation, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Orthogonal polynomials satisfying fourth order differential equations
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1981Synopsis These polynomials, which are intimately connected with the Legendre, Laguerre and Jacobi polynomials, are orthogonal with respect to Stieltjes weight functions which are absolutely continuous on (− 1, 1), (0, ∞) and (0, 1), respectively, but which have jumps at some of the intervals' ends.
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Conjugate Points for Fourth Order Linear Differential Equations
SIAM Journal on Applied Mathematics, 1972Let $r_{i_1 \,i_2 \cdots i_k } = \infty $ mean that no nontrivial solution of $y^{( n )} + \sum\nolimits_{i = 0}^{n - 1} {p_i } ( x )y^{( i )} = 0$ has an $i_1 - i_2 - \cdots - i_k $ distribution of zeros. The main result is the following theorem. THEOREM 1. If$n = 4$and$r_{121} = \infty $, then$r_{31} = r_{31} = \infty $and$\eta _k (
Ridenhour, Jerry R., Sherman, Thomas L.
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