Positive solutions to fractional boundary-value problems with p-Laplacian on time scales
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DOI: 10.1186/s13661-018-0990-2
Abstract: AbstractIn this article, we consider the following boundary-value problem of nonlinear fractional differential equation with p-Laplacian operator: Dα(ϕp(Dαu(t)))=f(t,u(t)),t∈[0,1]T,u(0)=u(σ(1))=Dαu(0)=Dαu(σ(1))=0, $$\begin{aligned}& D^{\alpha }\bigl(\phi_{p}\bigl(D^{\alpha }u(t)\bigr)\bigr)= f \bigl(t, u(t)\bigr),\quad t\in [0,1]_{T}, \\& u(0)= u\bigl(\sigma (1)\bigr)= D^{\alpha }u(0)= D^{\alpha }u\bigl(\sigma… read more here.
Keywords: bigl; time scales; positive solutions; value ... See more keywords
Asymptotics and oscillation of higher-order functional dynamic equations with Laplacian and deviating arguments
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DOI: 10.1186/s13662-016-1065-2
Abstract: In this paper, we deal with the asymptotics and oscillation of the solutions of higher-order nonlinear dynamic equations with Laplacian and mixed nonlinearities of the form {rn−1(t)ϕαn−1[(rn−2(t)(⋯(r1(t)ϕα1[xΔ(t)])Δ⋯)Δ)Δ]}Δ+∑ν=0Npν(t)ϕγν(x(gν(t)))=0 $$\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
Oscillation of third order nonlinear damped dynamic equation with mixed arguments on time scales
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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… read more here.
Keywords: bigl; nonlinear damped; bigr; third order ... See more keywords
Oscillation for second-order half-linear delay damped dynamic equations on time scales
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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$$ \bigl[a(t) \bigl\vert x^{\Delta }(t) \bigr\vert ^{\lambda -1}x^{\Delta }(t) \bigr]^{\Delta }+b(t) \bigl\vert x ^{\Delta }(t) \bigr\vert ^{\lambda -1}x^{\Delta }(t)+p(t) \bigl\vert x \bigl(\delta (t) \bigr)… read more here.
Keywords: bigl; bigr; delta; vert ... See more keywords
Oscillation theorems for three classes of conformable fractional differential equations
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DOI: 10.1186/s13662-019-2247-5
Abstract: AbstractIn this paper, we consider the oscillation theory for fractional differential equations. We obtain oscillation criteria for three classes of fractional differential equations of the forms Tαt0x(t)+∑i=1mpi(t)x(τi(t))=0,t⩾t0,Tαt0(r(t)(Tαt0(x(t)+p(t)x(τ(t))))β)+q(t)xβ(σ(t))=0,t⩾t0, $$\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}}… read more here.
Keywords: bigl; bigr; oscillation; fractional differential ... See more keywords
Asymptotic analysis of positive solutions of first-order cyclic functional differential systems
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DOI: 10.1515/gmj-2016-0085
Abstract: Abstract The structure and the asymptotic behavior of positive increasing solutions of functional differential systems of the form x ′ ( t ) = p ( t ) φ α (… read more here.
Keywords: bigl; varphi; bigl bigr; functional differential ... See more keywords