In this paper, we investigate a semilinear elliptic equation that involves multiple Hardy-type terms and critical Hardy-Sobolev exponents. By the Moser iteration method and analytic techniques, the asymptotic properties of its nontrivial solutions at the singular points are investigated.

In this paper, we are going to investigate the canonical property of solutions of systems of differential equations having a singularity and turning point of even order. First, by a replacement, we transform the system to the Sturm-Liouville equation with turning point. Using of the asymptotic estimates provided by Eberhard, Freiling, and Schneider for a special fundamental system of solutions of the Sturm-Liouville equation, we study the infinite product representation of solutions of the systems. Then we transform the Sturm-Liouville equation with turning point to the equation with singularity, then we study the asymptotic behavior of its solutions. Such representations are relevant to the inverse spectral problem.

We study some global aspects of differential complex 2-forms and 3-forms on complex manifolds. We compute the cohomology classes represented by the sets of points on a manifold where such a form degenerates in various senses, together with other similar cohomological obstructions. Based on these results and a formula for projective representations, we calculate the degree of the projectivization of certain orbits of the representation $\Lambda^k\C^n$.