Existence of unbounded solutions of boundary value problems for singular differential systems on whole line

Boundary value problems

Xiaohui Yang¹  Yuji Liu² 

[1] Department of Computer, Guangdong Police College, Guangzhou, P.R. China;Department of Mathematics, Guangdong University of Finance and Economics, Guangzhou, P.R. China

关键词: singular second-order differential system with quasi-Laplacian operators on the whole line;    boundary value problem;    unbounded solution;    fixed point theorem;    34B10;    34B15;    35B10;   

DOI  :  10.1186/s13661-015-0300-1

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Motivated by (Kyoung and Yong-Hoon in Sci. China Math. 53:967-984, 2010) and (Chen and Zhang in Sci. China Math. 54:959-972, 2011), this paper is concerned with a boundary value problem of singular second-order differential systems with quasi-Laplacian operators on the whole line. By constructing a completely continuous nonlinear operator and using a fixed point theorem, sufficient conditions guaranteeing the existence of at least one unbounded solution are established. The methods used are standard, however, their exposition in the framework of such a kind of problems is new and skillful. Three concrete examples are given to illustrate the main theorem.

【 授权许可】

CC BY