Anti-periodic solutions for semilinear evolution equations

作者：Chen; YQ

来源：Journal of Mathematical Analysis and Applications, 2006, 315(1): 337-348.

DOI：10.1016/j.jmaa.2005.08.001

• semilinear evolution equation
• anti-periodic solution

In this paper, we study the existence problem of anti-periodic solutions for the following first order evolution equation: {u'(t) Au(t) partial derivative Gu(t) F(t, u(t)) = 0, a.e. t is an element of R; u(t T) = -u(t), t is an element of R, in a separable Hilbert space H, where A is a self-adjoint operator, partial derivative G is the gradient of G and F is a nonlinear mapping. An existence result is obtained under the assumptions that D(A) is compactly embedded into H, partial derivative G is a continuous bounded mapping in H and F is a continuous mapping bounded by a L-2 function, which extends some known results in [Y.Q. Chen et al., Anti-periodic solutions for semilinear evolution equations, J. Math. Anal. Appl. 273 (2002) 627-636] and [A. Haraux, Anti-petiodic solutions of some nonlinear evolution equations, Manuscripta Math. 63 (1989) 479-505].

• 出版日期2006-3-1
• 单位佛山科学技术学院