AUTONOMOUS AND NON-AUTONOMOUS UNBOUNDED ATTRACTORS IN EVOLUTIONARY PROBLEMS

The paper establishes, under (H1)–(H3) (and their nonautonomous analogues), that J := ⋂_{t≥0} S(t)Q is the unbounded attractor with the expected properties, identifies J with the maximal invariant set of past-bounded complete trajectories, proves attraction in E+-bounded slices, minimality, and PJ = E+ in the autonomous case, and develops the full pullback theory for J(t) in the nonautonomous case. These statements and proofs are consistent and well-supported in the PDF (e.g., assumptions and J are defined; main results are Theorem 3 for the autonomous setting and Theorem 11 for the nonautonomous setting; PJ = E+ is proven by a degree argument in Lemma 3) . The candidate solution reproduces most of these results, but crucially misapplies Ważewski’s principle in Part A6 by treating (H_R, Q\H_R) as a Ważewski pair; here the purported exit set is not a subset of H_R, contradicting the standard setup. The paper instead uses a correct Brouwer degree argument to obtain PJ = E+ . There is also a minor technical lapse in Part A1 where (H3) is invoked with Q (possibly unbounded); this is easily repaired by starting from a bounded B absorbed by Q. Aside from these issues, the candidate’s arguments mostly mirror the paper’s structure and conclusions.