Solvability of inhomogeneous boundary-value problems for fourth-order differential equations

Abstract

Some new oscillation criteria are established for the nonlinear damped differential equation (r(t)k₁(x,x′))′+p(t)k₂(x,x′)x′+q(t)f(x(t))=0,t≥t0. The results obtained extend and improve some existing results in the literature.Встановлено деякi новi осциляцiйнi критерiї для згасаючого нелiнiйного рiвняння (r(t)k₁(x,x′))′+p(t)k₂(x,x′)x′+q(t)f(x(t))=0,t≥t0. Отриманi результати узагальнюють i посилюють деякi iснуючi результати.