Project supported by the Natural Science Foundation of Zhejiang Province.
Let ΩR^N(N≥4) be a bounded domain with smooth boundary Ω. In this note, we shall prove the existence of a nontrivial solution of the following semilinear elliptic equation with critical Sobolev exponent where a(x),...
Project supported by the National Natural Science Foundation of China.
A. Grzegorczyk listed in [1] nine important open problems, of which the seventh has been answered positively by R. W. Ritchie. Now, we shall answer negatively the ninth
A matrix A∈Rnn is called an M-matrix if A = sI- B, where B≥0 and s≥ρ(B), the spectral radius of B. By Γ(A) we denote the directed graph associated with a matrix A. The reflexive-transitive closure ...
We shall study such a finite group G with π_e(G)={1,p,q ,…. ,r,m }, where π_e(G)denotes the set of orders of elements in G andp, q, …, r are primes. We call the above groupthe EPMO-group. Theorem 1. Let G be a sol...
Applying Nevanlinna’s theory, R. Nevanlinna obtained the unicity theorem of meromorphic functions, G. Valiron and He Yuzan obtained the unicity theorem of transcendental algebroid functions. But for non-transcendenta...
In [1], Shevrin posed two open problems on semigroups: (1) Is a semigroup every subsemigroup of which can be included in a finite ideal series nilpotent? (2) Is a semigroup whose proper subsemigroups all are nilpotent...
where τ (K, u)is the distance between the two parallel hyperplanes of support to K, which are perpendicular to the given unit vector u and contain K between them.In 1974, T. Salle proposed a problem: What is the simp...
It was A. N. Prior who introduced the system MIPC in his monograph Time and Modality in 1957, which is of type S5 in the sense of R. A. Bull, i. e. adding the law of excluded middle to it yields S5. Many different mod...
Project supported by the National Natural Science Foundation of China.
Let H be a separable complex Hilbert space, and T an injective unilateral weighted shift with the weight sequence {wn} on H. Now we define the inverse weight shift T1 of T by T1en...