Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4633663 | Applied Mathematics and Computation | 2009 | 8 Pages |
Abstract
In this paper, by using Krasnosel'skii fixed-point theorem and under suitable conditions, we present the existence and multiplicity of nonnegative doubly periodic solutions for the following system:utt-uxx+c1ut+a11(t,x)u+a12(t,x)v=b1(t,x)f(t,x,u,v),vtt-vxx+c2vt+a21(t,x)u+a22(t,x)v=b2(t,x)g(t,x,u,v),where ci>0 is a constant, a11(t,x),a22(t,x),b1(t,x),b2(t,x)âC(R2,R+),a12(t,x),a21(t,x)âC(R2,R-),f(t,x,u,v),g(t,x,u,v)âC(R2ÃR+ÃR+,R+), and aij,bi,f,g are 2Ï-periodic in t and x. We derive two explicit intervals of b1(t,x) and b2(t,x) such that for any b1(t,x) and b2(t,x) in the two intervals respectively, the existence of at least one solution for the system is guaranteed, and the existence of at least two solutions for b1(t,x) and b2(t,x) in appropriate intervals is also discussed.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Fanglei Wang, Wanjun Li, Yukun An,