ASYMPTOTICALLY PERIODIC SOLUTIONS FOR DIFFERENTIAL AND DIFFERENCE INCLUSIONS IN HILBERT SPACES

作者：Morosanu Gheorghe^*; Ozpinar Figen

来源：Electronic Journal of Differential Equations, 2013, 06.

• Differential inclusion
• difference inclusion
• subdifferential
• maximal monotone operator
• weak convergence
• strong convergence

Let H be a real Hilbert space and let A : D (A) subset of H -> H be a (possibly set-valued) maximal monotone operator. We investigate the existence of asymptotically periodic solutions to the differential equation (inclusion) u'(t) + Au(t) (sic) f(t) + g (t), t > 0, where f is an element of L-loc(2) (R+, H) is a T-periodic T > 0) and g is an element of L-1 (R+, H). Consider also the following difference inclusion (which is a discrete analogue of the above inclusion): Delta u(n) + c(n)Au(n) (+ 1) (sic) f(n) + g(n), n = 0, 1, ... , where (c(n)) subset of (0, +infinity), (f(n)) subset of H are p-periodic sequences for a positive integer p and (g(n)) is an element of l(1)(H). We investigate the weak or strong convergence of its solutions to p-periodic sequences. We show that the previous results due to Baillon, Haraux (1977) and Djafari Rouhani, Khatibzadeh (2012) corresponding to g equivalent to 0, respectively g(n) = 0, n = 0, 1, ... , remain valid for g is an element of L-1(R+, H), respectively (g(n)) is an element of l(1)(H).

• 出版日期2013-1-8