Oscillation criteria for second order nonlinear differential equation with damping

1IntroductionandProblem Thefollowingisthesecondordernonlineardifferentialequationwithdamping: [p(t)ψ(y)u(y′)]′ r(t)y′(t) q(t)f(y)g(y′)=0(t≥t0),(1) inwhich,p(t)∈C′([t0,∞),(0,∞)),r(t)∈C([t0,∞),(-∞,∞)),q(t)∈C([t0, ∞),[0,∞))withtheexistenceofT≥t0,q(t)≠0,t∈[T,∞),f(y),g(y),ψ(y),u(y) ∈C((-∞,∞),(-∞,∞)),andyf(y)>0,yu(y)>0,y≠0. Thesolutiony(t)ofEq.(1)iscallednormalsolutionify(t)isthenon_constantsolutionof Eq.(1)andsupt≥t0｜y(t)｜>0(refertoRef.[1]).Anormalsolutionisoscill…