In this paper, by using the theory of cone, some results for fixed point index about a class of nonlinear operators which are not cone mappings are obtained. Some applications to boundary value problems for nonlinear elliptic partial differential equations are given.
is allowed. By applying Krasnosel'skii fixed point theorem of cone expansion-compression type, the existence of finitely or infinitely many positive solutions is established.
for super critical case s > 1 + 2/p, 1 < p < +∞, 1≤q≤+∞, and critical case s = 1 + 2/p with p∈(1,+∞) and q = 1. The blow-up criteria of the local solutions constructed are also obtained, which improves the Beale--Kato--Majda type criterion in homogeneous Besov space 
. Moreover, our blow-up criteria are only imposed on ∇θ.
In this paper, we formulate a free boundary problem with respect to a chemotaxis system, and then establish the local existence of the weak solutions for this free boundary problem.
In this paper, the definition of uniform strongly additive for a collection of strongly additive set-valued measures is introduced by on equivalent statement about the strongly additive set-valued measure. Then the Vitali--Hahn--Saks--Nikodym theorem about set-valued measure is established.
, and hypersingular integrals along Homogeneous curves be defined by 
The purpose of this paper is to investigate the boundedness of these integral operators on general modulation spaces.
In this paper, the authors establish some boundedness of Calderón--Zygmund type operators and their commutators generated by BMO functions or Lipschitz functions on Herz-type Hardy spaces.
. We establish a frame and dual frame-preservation theorem between affine systems and quasi-affine systems, and obtain a Fourier-domain characterization of affine (quasi-affine) dual wavelet frames without any decay assumptions. Furthermore, we also obtain a Fourier-domain characterization of affine Parseval frames.
Two identities obtained by means of the method of combining inverse technique and series rearrangement are introduced, which contain some famous identities, e.g. Rogers--Amanujan identities, as the special cases.
In this paper, we investigate the Riemann--Hilbert boundary value problems for n order Moisil--Theodoresc type equations, obtain the general solutions and the solvable conditions of the problems respectively in different cases.
We consider the differential Harnack inequalities for heat equations with potentials on Kähler manifolds under Kähler--Ricci flow, and get the monotonicity of corresponding W and F functionals by using them.
In this paper, a new concise proof is given for the following result: all the finite-dimensional restricted representations of a given restricted Lie superalgebra are completely reducible if and only if the even part is a torus and the odd part vanishes. This covers the corresponding result in the theory of Lie algebra.
