Boundedness problem for solutions of semilinear asymmetric equations

摘要

In this paper, we consider the boundedness problem for the solutions of the following semilinear differential equation(ϕp(x′))′+(p−1)[αϕp(x+)−βϕp(x−)]+g(x)=e(t)where ϕp(u)=|u|p−2u, p⩾2,α,β are positive constants satisfying α−(1/p)+β−(1/p)=2ω−1, g(x)∈C∞(R) is semilinear and e(t)∈C∞(R/Z).