This paper is concerned with the following fractional Schrodinger-Poisson system:{-(Δ)^(s)u+u+φu=λf(u)in R^(3)-(Δ)^(α)φu=u^(2)in R^(3)where s∈(3/4,1),α∈(0,1),λis a positive parameter,(-△)^(s),(-△)^(α)are ...This paper is concerned with the following fractional Schrodinger-Poisson system:{-(Δ)^(s)u+u+φu=λf(u)in R^(3)-(Δ)^(α)φu=u^(2)in R^(3)where s∈(3/4,1),α∈(0,1),λis a positive parameter,(-△)^(s),(-△)^(α)are fractional Laplacian operators.Under certain assumptions on f,we obtain the existence of at least one nontrivial solution of the system by using the methods of perturbation and Moser iterative method.展开更多
In this paper, we deal with the existence and multiplicity of solutions to the frac- tional elliptic problems involving critical and supercritical Sobolev exponent via variational arguments. By means of the truncation...In this paper, we deal with the existence and multiplicity of solutions to the frac- tional elliptic problems involving critical and supercritical Sobolev exponent via variational arguments. By means of the truncation combining with the Moser iteration, we prove that our problem has at least three solutions.展开更多
For a class of three-dimensional quasilinear wave equations with small initial data, we give a complete asymptotic expansion of the lifespan of classical solutions, that is, we solve a conjecture posed by John and H r...For a class of three-dimensional quasilinear wave equations with small initial data, we give a complete asymptotic expansion of the lifespan of classical solutions, that is, we solve a conjecture posed by John and H rmander. As an application of our result, we show that the solution of three- dimensional isentropic compressible Euler equations with irrotational initial data which are a small perturbation from a constant state will develop singularity in the first-order derivatives in finite time while the solution itself is continuous. Furthermore, for this special case, we also solve a conjecture of Alinhac.展开更多
For two-dimensional irrotational compressible Euler equations with initial data where that is a small perturbation from a constant state, we prove that the first-order derivatives of ρ, υ blow-up at the blow-up time...For two-dimensional irrotational compressible Euler equations with initial data where that is a small perturbation from a constant state, we prove that the first-order derivatives of ρ, υ blow-up at the blow-up time, while ρ, υ remain continuous. In particular, in the irrotational case we prove S. Alinhac’s statement.展开更多
We study the following coupled system of quasilinear equations:Under some assumptions on the nonlinear terms f and g, we establish some results about the existence and regularitl of vector solutions for the p-Laplacia...We study the following coupled system of quasilinear equations:Under some assumptions on the nonlinear terms f and g, we establish some results about the existence and regularitl of vector solutions for the p-Laplacian systems by using variational methods. In particular, we get two pairs of nontrivial solutions. We also study the different asymptotic behavior of solutions as the coupling parameter λ tends to zero.展开更多
文摘This paper is concerned with the following fractional Schrodinger-Poisson system:{-(Δ)^(s)u+u+φu=λf(u)in R^(3)-(Δ)^(α)φu=u^(2)in R^(3)where s∈(3/4,1),α∈(0,1),λis a positive parameter,(-△)^(s),(-△)^(α)are fractional Laplacian operators.Under certain assumptions on f,we obtain the existence of at least one nontrivial solution of the system by using the methods of perturbation and Moser iterative method.
基金Supported by NSFC(11371282,11201196)Natural Science Foundation of Jiangxi(20142BAB211002)
文摘In this paper, we deal with the existence and multiplicity of solutions to the frac- tional elliptic problems involving critical and supercritical Sobolev exponent via variational arguments. By means of the truncation combining with the Moser iteration, we prove that our problem has at least three solutions.
基金Project supported by the Zheng Ge Ru FoundationTianyuan Foundation of China
文摘For a class of three-dimensional quasilinear wave equations with small initial data, we give a complete asymptotic expansion of the lifespan of classical solutions, that is, we solve a conjecture posed by John and H rmander. As an application of our result, we show that the solution of three- dimensional isentropic compressible Euler equations with irrotational initial data which are a small perturbation from a constant state will develop singularity in the first-order derivatives in finite time while the solution itself is continuous. Furthermore, for this special case, we also solve a conjecture of Alinhac.
基金Project supported by the Tianyuan Foundation of ChinaLab. of Math, for Nonlinear Problems. Fudan. Univ.
文摘For two-dimensional irrotational compressible Euler equations with initial data where that is a small perturbation from a constant state, we prove that the first-order derivatives of ρ, υ blow-up at the blow-up time, while ρ, υ remain continuous. In particular, in the irrotational case we prove S. Alinhac’s statement.
文摘We study the following coupled system of quasilinear equations:Under some assumptions on the nonlinear terms f and g, we establish some results about the existence and regularitl of vector solutions for the p-Laplacian systems by using variational methods. In particular, we get two pairs of nontrivial solutions. We also study the different asymptotic behavior of solutions as the coupling parameter λ tends to zero.
