By variational methods, for a kind of Yamabe problem whose scalar curvature vanishes in the unit ball BN and on the boundary S^N-1 the mean curvature is prescribed, we construct multi-peak solutions whose maxima are l...By variational methods, for a kind of Yamabe problem whose scalar curvature vanishes in the unit ball BN and on the boundary S^N-1 the mean curvature is prescribed, we construct multi-peak solutions whose maxima are located on the boundary as the parameter tends to 0^＋ under certain assumptions. We also obtain the asymptotic behaviors of the solutions.展开更多
This paper is concerned with the harmonic equation(P;) : ?u = 0, u > 0 in B;and ?u/?ν+(（n-2）/2)u =(（n-2）/2) Ku;on S;where B;is the unit ball in R;, n ≥ 4 with Euclidean metric g;, ?B;= S;is its boundary, K is...This paper is concerned with the harmonic equation(P;) : ?u = 0, u > 0 in B;and ?u/?ν+(（n-2）/2)u =(（n-2）/2) Ku;on S;where B;is the unit ball in R;, n ≥ 4 with Euclidean metric g;, ?B;= S;is its boundary, K is a function on S;and ε is a small positive parameter. We construct solutions of the subcritical equation(P;) which blow up at one critical point of K. We give also a sufficient condition on the function K to ensure the nonexistence of solutions for(P;) which blow up at one point. Finally, we prove a nonexistence result of single peaked solutions for the supercritical equation(P;).展开更多
In this paper we prove an existence result for the nonlinear elliptic problem：-△u = Ku5,u 〉 0 in Ω,u = 0 on Ω,where Ω is a smooth bounded domain of R3 and K is a positive function in Ω.Our method relies on stud...In this paper we prove an existence result for the nonlinear elliptic problem：-△u = Ku5,u 〉 0 in Ω,u = 0 on Ω,where Ω is a smooth bounded domain of R3 and K is a positive function in Ω.Our method relies on studying its corresponding subcritical approximation problem and then using a topological argument.展开更多
The problem of prescribing scalar curvature in S^2 is discussed, and the solvability of the equation - ΔU + 2-Re^U= 0 on S^2, is given, where R ∈ C^0 (S^2). It is known that there are some obstructions. Some new res...The problem of prescribing scalar curvature in S^2 is discussed, and the solvability of the equation - ΔU + 2-Re^U= 0 on S^2, is given, where R ∈ C^0 (S^2). It is known that there are some obstructions. Some new results are given by seeking a solution of the minimax type. For example, supposing that R is G symmetric and is constant on the set of fixed points on S^2 under G ( where G is a subgroup of O (3)), it is proved that the equation is solvable if and only if R is positive somewhere.展开更多
Nanotubes form clusters and are found in curved bundles in nano-tube films and nanocomposites.Separation phenomenon is sus-pected to occur in these curved bundles.In this study,the deformation of a single-wall carbon ...Nanotubes form clusters and are found in curved bundles in nano-tube films and nanocomposites.Separation phenomenon is sus-pected to occur in these curved bundles.In this study,the deformation of a single-wall carbon nanotube(SWCNT)interacting with curved bundle nanotubes is analyzed.It is assumed that the bundle is rigid and only van der Waals force acts between the nanotube and the bundle of nanotubes.A new method of model-ing geometric nonlinear behavior of the nanotube due to finite rotation and the corresponding van der Waals force is developed using co-rotational finite element method(CFEM)formulation,combined with small deformation beam theory,with the inclusion of axial force.Current developed CFEM method overcomes the limitation of linear Finite Element Method(FEM)formulation regarding large rotations and deformations of carbon nanotubes.This study provides a numerical tool to identify the critical curvature influence on the interaction of carbon nanotubes due to van der Waals forces and can provide more insight into studying irregula-rities in the electronic transport properties of adsorbed nanotubes in nanocomposites.展开更多
The existence of infinitely many solutions of the following Dirichlet problem for p-mean curvature operator:-div((1+|u| 2) p-22u)=f(x,u),\ x∈Ω, u∈W 1,p 0(Ω),is considered, where Ω is a bounded domain in ...The existence of infinitely many solutions of the following Dirichlet problem for p-mean curvature operator:-div((1+|u| 2) p-22u)=f(x,u),\ x∈Ω, u∈W 1,p 0(Ω),is considered, where Ω is a bounded domain in R n(n>p>1) with smooth boundary Ω.Under some natural conditions together with some conditions weaker than (AR) condition,we prove that the above problem has infinitely many solutions by a symmetric version of the Mountain Pass Theorem if f(x,u)|u| p-2u→+∞ as u→∞.展开更多
基金the National Natural Science Foundation of China(No.10631030)Science Fund for Creative Research Groups of Natural Science Foundation of China(No.10721101)+3 种基金Chinese Academy of Sciences grant KJCX3-SYW-S03Program for New Century Excellent Talents in University(No.07-0350)the Key Project of Chinese Ministry of Education(No.107081)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry.
文摘By variational methods, for a kind of Yamabe problem whose scalar curvature vanishes in the unit ball BN and on the boundary S^N-1 the mean curvature is prescribed, we construct multi-peak solutions whose maxima are located on the boundary as the parameter tends to 0^＋ under certain assumptions. We also obtain the asymptotic behaviors of the solutions.
基金the Deanship of Scientific Research at Taibah University on material and moral support in the financing of this research project
文摘This paper is concerned with the harmonic equation(P;) : ?u = 0, u > 0 in B;and ?u/?ν+(（n-2）/2)u =(（n-2）/2) Ku;on S;where B;is the unit ball in R;, n ≥ 4 with Euclidean metric g;, ?B;= S;is its boundary, K is a function on S;and ε is a small positive parameter. We construct solutions of the subcritical equation(P;) which blow up at one critical point of K. We give also a sufficient condition on the function K to ensure the nonexistence of solutions for(P;) which blow up at one point. Finally, we prove a nonexistence result of single peaked solutions for the supercritical equation(P;).
文摘In this paper we prove an existence result for the nonlinear elliptic problem：-△u = Ku5,u 〉 0 in Ω,u = 0 on Ω,where Ω is a smooth bounded domain of R3 and K is a positive function in Ω.Our method relies on studying its corresponding subcritical approximation problem and then using a topological argument.
文摘The problem of prescribing scalar curvature in S^2 is discussed, and the solvability of the equation - ΔU + 2-Re^U= 0 on S^2, is given, where R ∈ C^0 (S^2). It is known that there are some obstructions. Some new results are given by seeking a solution of the minimax type. For example, supposing that R is G symmetric and is constant on the set of fixed points on S^2 under G ( where G is a subgroup of O (3)), it is proved that the equation is solvable if and only if R is positive somewhere.
基金This work was supported by the Texas Institute for the Intelligent Bio-Nano Materials and Structure for Aerospace Vehicles,funded by NASA[NCC-1-02038].
文摘Nanotubes form clusters and are found in curved bundles in nano-tube films and nanocomposites.Separation phenomenon is sus-pected to occur in these curved bundles.In this study,the deformation of a single-wall carbon nanotube(SWCNT)interacting with curved bundle nanotubes is analyzed.It is assumed that the bundle is rigid and only van der Waals force acts between the nanotube and the bundle of nanotubes.A new method of model-ing geometric nonlinear behavior of the nanotube due to finite rotation and the corresponding van der Waals force is developed using co-rotational finite element method(CFEM)formulation,combined with small deformation beam theory,with the inclusion of axial force.Current developed CFEM method overcomes the limitation of linear Finite Element Method(FEM)formulation regarding large rotations and deformations of carbon nanotubes.This study provides a numerical tool to identify the critical curvature influence on the interaction of carbon nanotubes due to van der Waals forces and can provide more insight into studying irregula-rities in the electronic transport properties of adsorbed nanotubes in nanocomposites.
基金Supported by the National Natural Science Foundation of China(1 0 1 71 0 3 2 ) and the GuangdongProvincial Natural Science Foundation(0 1 1 6 0 6 )
文摘The existence of infinitely many solutions of the following Dirichlet problem for p-mean curvature operator:-div((1+|u| 2) p-22u)=f(x,u),\ x∈Ω, u∈W 1,p 0(Ω),is considered, where Ω is a bounded domain in R n(n>p>1) with smooth boundary Ω.Under some natural conditions together with some conditions weaker than (AR) condition,we prove that the above problem has infinitely many solutions by a symmetric version of the Mountain Pass Theorem if f(x,u)|u| p-2u→+∞ as u→∞.
