Anti-periodic solutions for semilinear evolution equations

作者：Chen, YQ^*; Wang, XD; Xu, HX

来源：Journal of Mathematical Analysis and Applications, 2002, 273(2): 627-636.

DOI：10.1016/S0022-247X(02)00288-3

• BOUNDARY-VALUE-PROBLEMS
• DIFFERENTIAL-EQUATIONS
• ANTIPERIODIC SOLUTIONS

In this paper, we study the existence problem of anti-periodic solutions for the following first-order nonlinear evolution equation:
{u'(t) + Au(t) + F(t,u(t)) = 0, t is an element of R,
{u(t + T) = -u(t), t is an element of R,
in a Hilbert space H, where A is a self-adjoint operator and F is a continuous nonlinear operator. An existence result is obtained under assumptions that D(A) is compactly embedded into H and F is anti-periodic and bounded by a L-2 function. Furthermore, anti-periodic solutions for second-order equations are also studied.

• 出版日期2002-9-15
• 单位佛山科学技术学院