Boundedness of semilinear Duffing equations at resonance with oscillating nonlinearities

الأصل · EN

In this paper, we prove the boundedness of all the solutions for the equation x+n²x+g(x)+ψ'(x)=p(t) with the Lazer-Leach condition on g and p, where n∈ N+, p(t) and ψ'(x) are periodic and g(x) is bounded. For the critical situation that |∫₀²πp(t)eintdt |=2|g(+∞)-g(-∞)|, we also prove a sufficient and necessary condition for the boundedness if ψ'(x)≡0.