It is proved that if a nonlinear system possesses some group-symmetry, then under certain transversality it admits solutions with the corresponding symmetry. The method is due to Mawhin＇s guiding function one.
The existence of a zero for a holomorphic functions on a ball or on a rectangle under some sign conditions on the boundary generalizing Bolzano's ones for real functions on an interval is deduced in a very simple ...The existence of a zero for a holomorphic functions on a ball or on a rectangle under some sign conditions on the boundary generalizing Bolzano's ones for real functions on an interval is deduced in a very simple way from Cauchy's theorem for holomorphic functions. A more complicated proof, using Cauchy's argument principle, provides uniqueness of the zero, when the sign conditions on the boundary are strict. Applications are given to corresponding Brouwer fixed point theorems for holomorphic functions. Extensions to holomorphic mappings from C^n to C^n are obtained using Brouwer degree.展开更多
A two-point boundary value problem with a non-negative parameter Q arising inthe study of surface tension induced flow of a liquid metal or semiconductor is studied. We provethat the problem has at least one solution ...A two-point boundary value problem with a non-negative parameter Q arising inthe study of surface tension induced flow of a liquid metal or semiconductor is studied. We provethat the problem has at least one solution for Q ≥ 0. This improves a recent result that theproblem has at least one solution for 0 ≤ Q ≤ 13.21.展开更多
We obtain sufficient condition for the existence of periodic solutions of thefollowing second order functional differential equationsx'(t) + ax'~α(t) + bf(x(t)) + g(x(t-T_1), x'(t-T_2))=p(t)=p(t+2π).Our ...We obtain sufficient condition for the existence of periodic solutions of thefollowing second order functional differential equationsx'(t) + ax'~α(t) + bf(x(t)) + g(x(t-T_1), x'(t-T_2))=p(t)=p(t+2π).Our approach is based on the continuation theorem of coincidence degree, andthe α-priori: estimate of periodic solutions.展开更多
基金Supported by National Basic Research Program of China(grant No.2013CB834100)National Natural Science Foundation of China(grant No.11171132),and National Natural Science Foundation of China(grant No.11201173)
文摘It is proved that if a nonlinear system possesses some group-symmetry, then under certain transversality it admits solutions with the corresponding symmetry. The method is due to Mawhin＇s guiding function one.
文摘The existence of a zero for a holomorphic functions on a ball or on a rectangle under some sign conditions on the boundary generalizing Bolzano's ones for real functions on an interval is deduced in a very simple way from Cauchy's theorem for holomorphic functions. A more complicated proof, using Cauchy's argument principle, provides uniqueness of the zero, when the sign conditions on the boundary are strict. Applications are given to corresponding Brouwer fixed point theorems for holomorphic functions. Extensions to holomorphic mappings from C^n to C^n are obtained using Brouwer degree.
基金Supported by the Foundation of postdoctor of Huazhong University of Science and Technology
文摘A two-point boundary value problem with a non-negative parameter Q arising inthe study of surface tension induced flow of a liquid metal or semiconductor is studied. We provethat the problem has at least one solution for Q ≥ 0. This improves a recent result that theproblem has at least one solution for 0 ≤ Q ≤ 13.21.
基金The project is supported by NNSF of China(No.10271044)
文摘We obtain sufficient condition for the existence of periodic solutions of thefollowing second order functional differential equationsx'(t) + ax'~α(t) + bf(x(t)) + g(x(t-T_1), x'(t-T_2))=p(t)=p(t+2π).Our approach is based on the continuation theorem of coincidence degree, andthe α-priori: estimate of periodic solutions.
