Range of semilinear operators for systems at resonance - Amster, P. (2012)
For a vector function u: ℝ→ ℝ N we consider the system, where G: ℝ N → ℝ is a C 1 function. We are interested in finding all possible T-periodic forcing terms p(t) for which there is at least one solution. In other words, we examine the range of the semilinear operator S: H 2 per → L 2([0, T],ℝ N) given by, where. Writing p(t) = p̄ + p̄(t), where, we present several resultsconcerning the topological structure of the set. © 2012 Texas State University-San Marcos.