This paper mainly studied the semilinear biharmonic elliptic equation with multi-singularity and critical exponcnt,in which we mainly studied,where N≥5,k∈N,(λ_1,λ_2,…,λ_k)∈R~4,(a_1,a_2,"",a_k)∈R~(4n) and 2~*=2N/N-4 is the critical Sobolev exponent.

The boundedness is established on the Herz spaces and the weak Herz spaces for a large class of rough multilinear singular integrals T A bf(x)= p.

A numerical method for determination of multiple stress singularity orders and corresponding stress intensity coefficients is presented in this paper, by the example of plane problems with two stress singularity orders, based on the numerical solutions obtained by common numerical procedures such as FEM and BEM.

The continuity for multilinear singular integral operators on Hardy and Herz spaces;

Using the Fefferman-Stein inequality and the properties of the A∞ weight functions,the Sharp estimates are obtained and weighted inequalities above any weights for the multilinear singular integral operators with Dini type kernels.

In this paper,the boundedness for some multilinear singular integral operatorswith variable Calderón-Zygmund kernel on Hardy and Herz type Hardy spaces are obtained.

In this paper, the authors discusses a class of fractional multilinear singular integrals with rough kernels.

A class of multilinear oscillatory singular integral operators is studied and their boundedness on Lebesgue spaces L p(R)(1<p<∞) is obtained.