In this paper, we consider the unboundedness of solutions for the asymmetric equation x00＋ax＋？bx？＋？（x）ψ（x0）＋f（x）＋g（x0）=p（t）, where x＋ = max{x, 0}, x？ = max{？x, 0}, a and b are two different posit...In this paper, we consider the unboundedness of solutions for the asymmetric equation x00＋ax＋？bx？＋？（x）ψ（x0）＋f（x）＋g（x0）=p（t）, where x＋ = max{x, 0}, x？ = max{？x, 0}, a and b are two different positive constants, f （x） is locally Lipschitz continuous and bounded,？（x）, ψ（x）, g（x） and p（t） are continuous functions, p（t） is a 2π-periodic function. We discuss the existence of unbounded solutions under two classes of conditions： the resonance case √1a＋ √1b ∈Q and the nonresonance case√1a ＋ √1b /∈Q.展开更多
基金Supported by the Tianyuan Special Foundation（11526148） Supported by the National Natural Science Foundation of China（l1571187, 11461056）
文摘In this paper, we consider the unboundedness of solutions for the asymmetric equation x00＋ax＋？bx？＋？（x）ψ（x0）＋f（x）＋g（x0）=p（t）, where x＋ = max{x, 0}, x？ = max{？x, 0}, a and b are two different positive constants, f （x） is locally Lipschitz continuous and bounded,？（x）, ψ（x）, g（x） and p（t） are continuous functions, p（t） is a 2π-periodic function. We discuss the existence of unbounded solutions under two classes of conditions： the resonance case √1a＋ √1b ∈Q and the nonresonance case√1a ＋ √1b /∈Q.
