arXiv subjects

Fengying Li

Publications and source records attributed to Fengying Li.

12 recordsLinked to original sources

arXiv2021

A Generalized Mountain Pass Lemma with a Closed Subset for Locally Lipschitz Functionals

The classical Mountain Pass Lemma of Ambrosetti-Rabinowitz has been studied, extended and modified in several directions. Notable examples would certainly include the generalization to locally Lipschitz functionals by K.C. Chang, analyzing the structure of the critical set in the mountain pass theorem in the works of Hofer, Pucci-Serrin and Tian, and the extension by Ghoussoub-Preiss to closed subsets in a Banach space with recent variations. In this paper, we utilize the generalized gradient of Clarke and Ekeland's variatonal principle to generalize the Ghoussoub-Preiss's Theorem in the setting of locally Lipschitz functionals. We give an application to periodic solutions of Hamiltonian systems.

math.CA↗

arXiv2019

Solutions for fourth-order Kirchhoff type elliptic equations involving concave-convex nonlinearities in $\mathbb{R}^{N}$

In this paper, we show the existence and multiplicity of solutions for the following fourth-order Kirchhoff type elliptic equations \begin{eqnarray*} Δ^{2}u-M(\|\nabla u\|_{2}^{2})Δu+V(x)u=f(x,u),\ \ \ \ \ x\in \mathbb{R}^{N}, \end{eqnarray*} where $M(t):\mathbb{R}\rightarrow\mathbb{R}$ is the Kirchhoff function, $f(x,u)=λk(x,u)+ h(x,u)$, $λ\geq0$, $k(x,u)$ is of sublinear growth and $h(x,u)$ satisfies some general 3-superlinear growth conditions at infinity. We show the existence of at least one solution for above equations for $λ=0$. For $λ>0$ small enough, we obtain at least two nontrivial solutions. Furthermore, if $f(x,u)$ is odd in $u$, we show that above equations possess infinitely many solutions for all $λ\geq0$. Our theorems generalize some known results in the literatures even for $λ=0$ and our proof is based on the variational methods.

math.DS↗

arXiv2016

Generalized Mountain Pass Lemma Related with a Closed Subset and Locally Lipschitz Functionals

The classical Mountain Pass Lemma of Ambrosetti-Rabinowitz has been studied, extended and modified in several directions, notable examples would certainly include the generalization to locally Lipschitz functionals in K.C. Chang, analysis of the structure of the critical set in the mountain pass theorem by Hofer and Pucci-Serrin and Tian, the extension by Ghoussoub-Preiss to closed subsets in a Banach space, and variations found in the recent Peral . In this paper, we utilize the generalized gradient of Clarke and Ekeland's variational principle to generalize the Ghoussoub-Preiss's Theorem in the setting of locally Lipschitz functionals.

math.FA↗

arXiv2014

A Note on Homoclinic Orbits for Second Order Hamiltonian Systems

In this paper, we study the existence for the homoclinic orbits for the second order Hamiltonian systems. Under suitable conditions on the potential $V$, we apply the direct method of variations and the Fourier analysis to prove the existence of homoclinc orbits.

math.DS↗

arXiv2014

New Periodic Solutions of Singular Hamiltonian Systems with Fixed Energies

By using the variational minimizing method with a special constraint and the direct variational minimizing method without constraint, we study second order Hamiltonian systems with a singular potential $V\in C^2(R^n\backslash O,R)$ and $V\in C^1(R^2\backslash O,R)$ which may have an unbounded potential well, and prove the existence of non-trivial periodic solutions with a prescribed energy. Our results can be regarded as some complements of the well-known Theorems of Benci-Gluck-Ziller-Hayashi and Ambrosetti-Coti Zelati and so on.

math-ph↗

arXiv2014

Periodic Solutions of Non-Autonomous Second Order Hamiltonian Systems

We try to generalize a result of M. Willem on forced periodic oscillations which required the assumption that the forced potential is periodic on spatial variables. In this paper, we only assume its integral on the time variable is periodic, and so we extend the result to cover the forced pendulum equation. We apply the direct variational minimizing method and Rabinowtz's saddle point theorem to study the periodic solution when the integral of the potential on the time variable is periodic.

math.CA↗

arXiv2014

Periodic Solutions for $N$-Body-Type Problems

We consider non-autonomous $N$-body-type problems with strong force type potentials at the origin and sub-quadratic growth at infinity, and using Ljusternik-Schnirelmann theory, we prove the existence of unbounded sequences of critical values for the Lagrangian action corresponding to non-collision periodic solutions.

math-ph↗

arXiv2014

Some Applications of Generalized Mountain Pass Lemma

The Ghoussoub-Preiss's generalized Mountain Pass Lemma with Cerami-Palais-Smale type condition is a generalization of classical MPL of Ambrosetti-Rabinowitz, we apply it to study the existence of the periodic solutions with a given energy for some second order Hamiltonian systems with symmetrical and non-symmetrical potentials.

math.FA↗

arXiv2013

Notes on a Theorem of Benci-Gluck-Ziller-Hayashi

We use constrained variational minimizing methods to study the existence of periodic solutions with a prescribed energy for a class of second order Hamiltonian systems with a $C^2$ potential function which may have an unbounded potential well. Our result can be regarded as complementary to the well-known theorem of Benci-Gluck-Ziller and Hayashi.

math.CA↗

arXiv2012

Large Essential norm of Toeplitz operators and Hankel operators on the weighted Bergman space

In this paper, we show that on the weighted Bergman space of the unit disk the essential norm of a noncompact Hankel operator equals its distance to the set of compact Hankel operators and is realized by infinitely many compact Hankel operators, which is analogous to the theorem of Axler, Berg, Jewell and Shields on the Hardy space in Axler et al. (1979); moreover, the distance is realized by infinitely many compact Hankel operators with symbols continuous on the closure of the unit disk and vanishing on the unit circle.

math.FA↗

arXiv2012

Nonplanar Periodic Solutions for Spatial Restricted N+1-Body Problems

We use variational minimizing methods to study spatial restricted N+1-body problems with a zero mass moving on the vertical axis of the moving plane for N equal masses. We prove that the minimizer of the Lagrangian action on the anti-T/2 or odd symmetric loop space must be a non-planar periodic solution for any $N\geq2$.

math-ph↗

arXiv2006

B\to X_sγ, X_s l^+ l^- decays and constraints on the mass insertion parameters in the MSSM

In this paper, we study the upper bounds on the mass insertion parameters $(δ^{q}_{AB})_{ij}$ in the minimal supersymmetric standard model (MSSM). We found that the information from the measured branching ratio of $B \to X_s l^+ l^-$ decay can help us to improve the upper bounds on the mass insertions parameters $\left (δ^{u,d}_{AB})_{3j,i3}$. Some regions allowed by the data of $Br(B \to X_s γ) $ are excluded by the requirement of a SM-like $C_{7γ}(m_b)$ imposed by the data of $Br(B \to X_s l^+ l^-)$.

hep-ph↗