Nonnegative doubly periodic solutions for nonlinear telegraph system

作者：Wang Fanglei^*; An Yukun

来源：Journal of Mathematical Analysis and Applications, 2008, 338(1): 91-100.

DOI：10.1016/j.jmaa.2007.05.008

• telegraph system
• doubly periodic solution
• cone
• fixed point theorem

This paper deals with the nonnegative doubly periodic solutions for nonlinear telegraph system
{u(tt) - u(xx) + c(1)u(t) + a(11) (t, x)u + a(12) (t, x)v = b(1) (t, x)f (t, x, u, v), v(tt) - v(xx) + c(2) v(t) + a(21) (t, x)u + a(22) (t, x)v = b(2)(t, x)g(t, x, u, v),
where c(i) > 0 is a constant, a(11), a(22), b(1), b(2) is an element of C(R-2, R+), a(12), a(21) E C(R-2, R-), f, g is an element of C(R-2 x R+ x R+, R+), and a(ij), b(i), f, g are 2 pi-periodic in t and x. We show the existence and multiplicity results when 0 <= a(tt)(t, x) <= c(i)(2)/4and f, g are superlinear or sublinear on (u, v) by using the fixed point theorem in cones.

• 出版日期2008-2-1
• 单位南京大学