Results 1 to 10 of about 82 (79)
Journal of MathematicsIn this article, by using the fixed point index theory, we investigate the existence of positive solutions for Riemann–Liouville nabla fractional difference equations satisfying two distinct types of boundary conditions.
Jagan Mohan Jonnalagadda +1 more
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From Hardy to Rellich inequalities on graphs
Proceedings of the London Mathematical Society, Volume 122, Issue 3, Page 458-477, March 2021., 2021 Abstract We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These weights involve the Hardy weight and a function which satisfies an eikonal inequality.
Matthias Keller +2 more
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A certain class of fractional difference equations with damping: Oscillatory properties
Demonstratio Mathematica, 2023 In this study, we have investigated the oscillatory properties of the following fractional difference equation: ∇α+1χ(κ)⋅∇αχ(κ)−p(κ)г(∇αχ(κ))+q(κ)G∑μ=κ−α+1∞(μ−κ−1)(−α)χ(μ)=0,{\nabla }^{\alpha +1}\chi \left(\kappa )\cdot {\nabla }^{\alpha }\chi \left ...
Arundhathi Sivakumar +3 more
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Open Mathematics, 2022 In this article, we consider a discrete nonlinear third-order boundary value problem Δ3u(k−1)=λa(k)f(k,u(k)),k∈[1,N−2]Z,Δ2u(η)=αΔu(N−1),Δu(0)=−βu(0),u(N)=0,\left\{\phantom{\rule[-1.25em]{}{0ex}}\begin{array}{l}{\Delta }^{3}u\left(k-1)=\lambda a\left(k)f ...
Li Huijuan +2 more
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Asymptotic behavior of solutions of a second-order nonlinear discrete equation of Emden-Fowler type
Advances in Nonlinear Analysis, 2023 The article investigates a second-order nonlinear difference equation of Emden-Fowler type Δ2u(k)±kαum(k)=0,{\Delta }^{2}u\left(k)\pm {k}^{\alpha }{u}^{m}\left(k)=0, where kk is the independent variable with values k=k0,k0+1,…k={k}_{0},{k}_{0}+1,\ldots ...
Diblík Josef, Korobko Evgeniya
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Open Mathematics, 2021 In this paper, we discuss the existence of positive solutions to a discrete third-order three-point boundary value problem. Here, the weight function a(t)a\left(t) and the Green function G(t,s)G\left(t,s) both change their sign.
Cao Xueqin, Gao Chenghua, Duan Duihua
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, 2023 In this paper, we investigate the relations between the growth of entire coefficients and that of solutions of complex homogeneous and non-homogeneous linear difference equations with entire coefficients of φ-order by using a slow growth scale, the φ ...
Pulak Sahoo +3 more
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A coupled system of fractional difference equations with anti-periodic boundary conditions
, 2023 In this article, we give sufficient conditions for the existence, uniqueness and Ulam–Hyers stability of solutions for a coupled system of two-point nabla fractional difference boundary value problems subject to anti-periodic boundary conditions, using ...
Jagan Mohan Jonnalagadda +1 more
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A unified approach for novel estimates of inequalities via discrete fractional calculus techniques
Alexandria Engineering Journal, 2022 In this article, we introduce the discrete fractional sum equations and inequalities. Some new generalized Grüss type discrete fractional sum inequalities are developed. We employ a nabla or backward difference; we employ the Riemann-Liouville definition
Samaira Naz, Yu-Ming Chu
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Open Mathematics, 2022 In this article, we are concerned with the periodic solutions of first-order difference equation Δu(t−1)=f(t,u(t))−s,t∈Z,(P)\Delta u\left(t-1)=f\left(t,u\left(t))-s,\hspace{1em}t\in {\mathbb{Z}},\hspace{1.0em}\hspace{1.0em}\left(P) where s∈Rs\in {\mathbb{
Zhao Jiao, Ma Ruyun
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