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Zhaosheng Feng

Publications and source records attributed to Zhaosheng Feng.

6 recordsLinked to original sources
arXiv2025

Quasi-periodic response solutions of nonlinear plate models with nonlocal energy damping

Response solutions are quasi-periodic ones with the same frequency as the forcing term. The present work is devoted to constructing response solutions for $d$-dimensional nonlinear plate models with nonlocal energy damping, which are closely related to damping phenomena in flight structures. For such models, the main characteristic is that the dissipation rate depends on the energy strength. By considering a small parameter $ε$ in the domain excluding the origin and imposing a small quasi-periodic forcing with a Diophantine frequency vector, we demonstrate the persistence of the corresponding response solution. We provide an alternative approach to the contraction mapping principle (cf. [7, 33]) through a combination of reduction together with the Nash--Moser iteration technique. The reason behind this approach lies in the derivative losses caused by the nonlocal nonlinearity.

math.AP↗
arXiv2023

Normalized solutions for Sobolev critical Schrödinger-Bopp-Podolsky systems

We study the Sobolev critical Schrödinger-Bopp-Podolsky system \begin{gather*} -Δu+ϕu=λu+μ|u|^{p-2}u+|u|^4u\quad \text{in }\mathbb{R}^3, -Δϕ+Δ^2ϕ=4πu^2\quad \text{in } \mathbb{R}^3, \end{gather*} under the mass constraint \[ \int_{\mathbb{R}^3}u^2\,dx=c \] for some prescribed $c>0$, where $2 0$ is a parameter, and $λ\in\mathbb{R}$ is a Lagrange multiplier. By developing a constraint minimizing approach, we show that the above system admits a local minimizer. Furthermore, we establish the existence of normalized ground state solutions.

math.AP↗
arXiv2021

Multiple positive solutions for the fractional Schrödinger-Poisson systems involving critical nonlinearities with potential

In this paper, we study the existence of multiple positive solutions for a class of fractional Schrödinger-Poisson systems involving sign-changing potential and critical nonlinearities on an unbounded domain. With the help of Nehari manifold and Ljusternik-Schnirelmann category, we investigate how the coefficient $g(x)$ of the critical nonlinearity affects the number of positive solutions. Moreover, we present a novel relationship between the number of positive solutions and the category of the global maximum set of $g(x)$.

math.AP↗
arXiv2021

Positive solutions for the fractional Schrödinger equations with logarithmic and critical nonlinearities

In this paper, we study a class of fractional Schrödinger equations involving logarithmic and critical nonlinearities on an unbounded domain, and show that such an equation with positive or sign-changing weight potentials admits at least one positive ground state solution and the associated energy is positive (or negative). By applying the Nehari manifold method and Ljusternik-Schnirelmann category, we deeply investigate how the weight potential affects the multiplicity of positive solutions, and obtain the relationship between the number of positive solutions and the category of some sets related to the weight potential.

math.AP↗
arXiv2005

Coupled atomic motion and spin-glass transition in FeAl2

We have used 57Fe Mossbauer spectroscopy and x-ray diffraction to study the magnetic and vibrational properties of FeAl2. FeAl2 is an ordered intermetallic with a large Fe local moment, and a complex crystal structure with site-occupation disorder on some sites. This material exhibits spin-glass freezing below 35 K. From the 57Fe recoilless fraction, we find that there is a vibrational mode which freezes out concurrently with the spin freezing. X-ray powder diffraction measurements confirm this result, indicating an anomalous change in the Debye-Waller factor at temperatures below the spin-freezing temperature.

cond-mat.mtrl-sci↗