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Published in 2017 at "Journal of Inequalities and Applications"
DOI: 10.1186/s13660-017-1485-x
Abstract: In this paper, we present some extensions of interpolation between the arithmetic-geometric means inequality. Among other inequalities, it is shown that if A, B, X are n×n$n\times n$ matrices, then ∥AXB∗∥2≤∥f1(A∗A)Xg1(B∗B)∥∥f2(A∗A)Xg2(B∗B)∥, $$\begin{aligned} \bigl\Vert AXB^{*} \bigr\Vert…
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Keywords:
bigr;
vert bigl;
vert;
bigr vert ... See more keywords
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Published in 2017 at "Advances in Difference Equations"
DOI: 10.1186/s13662-016-1065-2
Abstract: In this paper, we deal with the asymptotics and oscillation of the solutions of higher-order nonlinear dynamic equations with Laplacian and mixed nonlinearities of the form {rn−1(t)ϕαn−1[(rn−2(t)(⋯(r1(t)ϕα1[xΔ(t)])Δ⋯)Δ)Δ]}Δ+∑ν=0Npν(t)ϕγν(x(gν(t)))=0 $$\begin{aligned}& \bigl\{ r_{n-1}(t) \phi_{\alpha_{n-1}} \bigl[ \bigl(r_{n-2}(t) \bigl(\cdots \bigl(r_{1}(t)\phi…
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bigl;
bigr;
equations laplacian;
higher order ... See more keywords
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Published in 2017 at "Advances in Difference Equations"
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…
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bigl;
order functional;
bigr;
order ... See more keywords
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Published in 2018 at "Advances in Difference Equations"
DOI: 10.1186/s13662-018-1654-3
Abstract: AbstractThe objective of this paper is to offer sufficient conditions for the oscillation of all solutions of the third order nonlinear damped dynamic equation with mixed arguments of the form (r2(r1(yΔ)α)Δ)Δ(t)+p(t)ψ(t,yΔ(a(t)))+q(t)f(t,y(g(t)))=0$$\bigl(r_{2}\bigl(r_{1}\bigl(y^{\Delta}\bigr)^{\alpha}\bigr)^{\Delta}\bigr)^{\Delta}(t)+p(t)\psi \bigl(t,y^{\Delta}\bigl(a(t)\bigr)\bigr)+q(t)f\bigl(t,y\bigl(g(t)\bigr) \bigr)=0 $$ on…
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bigl;
nonlinear damped;
bigr;
third order ... See more keywords
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Published in 2019 at "Advances in Difference Equations"
DOI: 10.1186/s13662-019-2136-y
Abstract: AbstractWe investigate oscillation of second-order half-linear variable delay damped dynamic equations [a(t)|xΔ(t)|λ−1xΔ(t)]Δ+b(t)|xΔ(t)|λ−1xΔ(t)+p(t)|x(δ(t))|λ−1x(δ(t))=0$$ \bigl[a(t) \bigl\vert x^{\Delta }(t) \bigr\vert ^{\lambda -1}x^{\Delta }(t) \bigr]^{\Delta }+b(t) \bigl\vert x ^{\Delta }(t) \bigr\vert ^{\lambda -1}x^{\Delta }(t)+p(t) \bigl\vert x \bigl(\delta (t) \bigr)…
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Published in 2019 at "Advances in Difference Equations"
DOI: 10.1186/s13662-019-2247-5
Abstract: AbstractIn this paper, we consider the oscillation theory for fractional differential equations. We obtain oscillation criteria for three classes of fractional differential equations of the forms Tαt0x(t)+∑i=1mpi(t)x(τi(t))=0,t⩾t0,Tαt0(r(t)(Tαt0(x(t)+p(t)x(τ(t))))β)+q(t)xβ(σ(t))=0,t⩾t0, $$\begin{aligned}& T_{\alpha}^{t_{0}} x(t)+\sum_{i=1}^{m}p_{i}(t)x \bigl(\tau_{i}(t)\bigr)=0,\quad t\geqslant t_{0}, \\& T_{\alpha}^{t_{0}}…
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bigr;
oscillation;
fractional differential ... See more keywords