Prolongation of solutions of measure differential equations and dynamic equations on time scales
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DOI: 10.1002/mana.201700420
Abstract: In this paper, we prove the results on existence and uniqueness of the maximal solutions for measure differential equations, considering more general conditions on functions f and g by using the correspondence between the solutions… read more here.
Keywords: time scales; solutions measure; differential equations; dynamic equations ... See more keywords
Oscillation for a nonlinear neutral dynamic equations on time‐scales with variable exponents
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DOI: 10.1002/mma.5636
Abstract: In the present manuscript, we study the oscillation theory for a first‐order nonlinear neutral dynamic equations on timescales with variable exponents of the form read more here.
Keywords: nonlinear neutral; dynamic equations; variable exponents; neutral dynamic ... See more keywords
Nonoscillation of half‐linear dynamic equations on time scales
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DOI: 10.1002/mma.7304
Abstract: The research contained in this paper belongs to the qualitative theory of dynamic equations on time scales. Via the detailed analysis of solutions of the associated Riccati equation and an advanced averaging technique, we provide… read more here.
Keywords: dynamic equations; time; nonoscillation half; equations time ... See more keywords
Hille and Nehari-Type Oscillation Criteria for Third-Order Emden–Fowler Neutral Delay Dynamic Equations
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DOI: 10.1007/s40840-016-0354-y
Abstract: We establish some oscillation criteria for the third-order Emden–Fowler neutral delay dynamic equations of the form: $$\begin{aligned} (a(t)(x(t)+r(t)x(\tau (t)))^{\Delta \Delta })^\Delta +p(t)x^\gamma (\delta (t))=0 \end{aligned}$$(a(t)(x(t)+r(t)x(τ(t)))ΔΔ)Δ+p(t)xγ(δ(t))=0on a time scale $$\mathbb {T}$$T, where $$\gamma >0$$γ>0 is a… read more here.
Keywords: dynamic equations; delay dynamic; neutral delay; oscillation criteria ... See more keywords
Dynamic equations for solid isotropic radially functionally graded circular cylinders
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DOI: 10.1016/j.compstruct.2018.03.087
Abstract: A hierarchy of dynamic equations for solid isotropic functionally graded circular cylinders is derived based on the three dimensional elastodynamic theory. The material parameters are assumed to vary in the radial direction. Using Fourier expansions… read more here.
Keywords: graded circular; functionally graded; equations solid; circular cylinders ... See more keywords
Boundedness of solutions of measure differential equations and dynamic equations on time scales
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DOI: 10.1016/j.jde.2017.02.008
Abstract: Abstract In this paper, we investigate the boundedness results for measure differential equations. In order to obtain our results, we use the correspondence between these equations and generalized ODEs. Furthermore, we prove our results concerning… read more here.
Keywords: time scales; boundedness solutions; differential equations; dynamic equations ... See more keywords
Oscillation constants for second-order nonlinear dynamic equations of Euler type on time scales
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Difference Equations and Applications"
DOI: 10.1080/10236198.2017.1371146
Abstract: Abstract We are concerned with the oscillation problem for second-order nonlinear dynamic equations on time scales of the form , where f(x) satisfies if . By means of Riccati technique and phase plane analysis of… read more here.
Keywords: nonlinear dynamic; second order; time scales; dynamic equations ... See more keywords
Dual Quaternions Representation of Lagrange's dynamic equations
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DOI: 10.1115/1.4062463
Abstract: Abstract' This paper introduces for the first time, the Lagrange's dynamic equations in dual number quaternion form. Additionally, Rayleigh's dissipation function in dual quaternion form is introduced here allowing for the accounting of dissipative (non-conservative)… read more here.
Keywords: dual quaternions; equations dual; representation lagrange; dynamic equations ... See more keywords
Asymptotic derivation of refined dynamic equations for a thin elastic annulus
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DOI: 10.1177/1081286520944980
Abstract: Low-frequency vibrations of a thin elastic annulus are considered. The dynamic equations of plane strain are subjected to asymptotic treatment beyond the leading-order approximation. The main peculiarity of the considered problem is a specific degeneration… read more here.
Keywords: asymptotic derivation; elastic annulus; dynamic equations; derivation refined ... See more keywords
Asymptotics and oscillation of higher-order functional dynamic equations with Laplacian and deviating arguments
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DOI: 10.1186/s13662-016-1065-2
Abstract: In this paper, we deal with the asymptotics and oscillation of the solutions of higher-order nonlinear dynamic equations with Laplacian and mixed nonlinearities of the form {rn−1(t)ϕαn−1[(rn−2(t)(⋯(r1(t)ϕα1[xΔ(t)])Δ⋯)Δ)Δ]}Δ+∑ν=0Npν(t)ϕγν(x(gν(t)))=0 $$\begin{aligned}& \bigl\{ r_{n-1}(t) \phi_{\alpha_{n-1}} \bigl[ \bigl(r_{n-2}(t) \bigl(\cdots \bigl(r_{1}(t)\phi… read more here.
Keywords: bigl; bigr; equations laplacian; higher order ... See more keywords
Oscillation criteria for third-order functional half-linear dynamic equations
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DOI: 10.1186/s13662-017-1164-8
Abstract: In this paper, we study the third-order functional dynamic equation {r2(t)ϕα2([r1(t)ϕα1(xΔ(t))]Δ)}Δ+q(t)ϕα(x(g(t)))=0,$$ \bigl\{ r_{2}(t)\phi_{\alpha_{2}} \bigl( \bigl[ r_{1}(t) \phi _{\alpha _{1}} \bigl( x^{\Delta}(t) \bigr) \bigr] ^{\Delta} \bigr) \bigr\} ^{\Delta}+q(t)\phi_{\alpha} \bigl( x\bigl(g(t)\bigr) \bigr) =0, $$ on an upper-unbounded… read more here.
Keywords: bigl; order functional; bigr; order ... See more keywords