Restriction of the Fourier Transform to Some Oscillating Curves
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DOI: 10.1007/s00041-017-9554-6
Abstract: Let $$\phi $$ϕ be a smooth function on a compact interval I. Let $$\begin{aligned} \gamma (t)=\left( t,t^2,\ldots ,t^{n-1},\phi (t)\right) . \end{aligned}$$γ(t)=t,t2,…,tn-1,ϕ(t).In this paper, we show that $$\begin{aligned} \left( \int _I \big |\hat{f}(\gamma (t))\big |^q \big… read more here.
Keywords: restriction; transform oscillating; end aligned; restriction fourier ... See more keywords
Whiskered Tori for Forced Beam Equations with Multi-dimensional Liouvillean Frequency
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DOI: 10.1007/s10884-019-09754-1
Abstract: In this paper we develop a Kolmogorov–Arnold–Moser (KAM) theory close to two fixed points for quasi-periodically forced nonlinear beam equation $$\begin{aligned} \begin{aligned} y_{tt}+my+y_{xxxx}=y^{3}+ \varepsilon f(\omega t,x,y),\ \ x\in [0,\ \pi ], \end{aligned} \end{aligned}$$ y tt… read more here.
Keywords: frequency; aligned xxxx; end aligned; begin aligned ... See more keywords
On the Asymptotic Stability for Nonlinear Oscillators with Time-Dependent Damping
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DOI: 10.1007/s12346-018-0294-z
Abstract: The equation $$\begin{aligned} x''+h(t,x,x')x'+f(x)=0 \qquad (x\in \mathbb {R},\ xf(x)\ge 0,\ t\in [0,\infty )) \end{aligned}$$x′′+h(t,x,x′)x′+f(x)=0(x∈R,xf(x)≥0,t∈[0,∞))is considered, where the damping coefficient h allows an estimate $$\begin{aligned} a(t)|x'|^\alpha w(x,x')\le h(t,x,x')\le b(t) W(x,x'). \end{aligned}$$a(t)|x′|αw(x,x′)≤h(t,x,x′)≤b(t)W(x,x′).Sufficient conditions on the lower and… read more here.
Keywords: stability nonlinear; oscillators time; nonlinear oscillators; asymptotic stability ... See more keywords
The Nonexistence of Positive Solutions for A Coupled System of Non-separated Boundary Value Problems
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DOI: 10.1007/s12591-019-00510-x
Abstract: In this paper, we consider the non-separated boundary value problem for system of nonlinear Riemann–Liouville fractional differential equations $$\begin{aligned} \begin{aligned} D_{0^+}^{\alpha }x(t)+\lambda f(t, x(t), y(t))=0,~~0 read more here.
Keywords: system; separated boundary; non separated; boundary value ... See more keywords
On Meromorphic Solutions of Functional Equations of Fermat Type
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DOI: 10.1007/s40840-018-0613-1
Abstract: Take complex numbers $$\alpha ,\beta ,c,a_j,b_j$$α,β,c,aj,bj$$(j=0,1,2)$$(j=0,1,2) such that $$c\ne 0$$c≠0 and $$\begin{aligned} \mathrm{rank} \left( \begin{array}{ccc} a_{0} &{} a_{1} &{} a_{2}\\ b_{0} &{} b_{1} &{} b_{2}\\ \end{array} \right) =2. \end{aligned}$$ranka0a1a2b0b1b2=2.We show that if the following functional… read more here.
Keywords: end aligned; fermat type; meromorphic solutions; alpha beta ... See more keywords