Boundedness of solutions for nonlinear differential equations

Abstract

In this paper, the boundedness of all the solutions for quasilinear differential equation (ϕ p(x′))′ + αϕ p(x +) − βϕ p(x −) + f(x) = e(t) is discussed, where ϕ p ( u) = { u} p−2 u, p ≥ 2 is fixed, αβ are positive constants, f( χ) is semilinear at infinity and e( t) is a 2π-periodic function.