Details

Autor(en) / Beteiligte

• Grace, S.R
• Lalli, B.S

Titel

Oscillation theorems for damped-forced nth order nonlinear differential equations with deviating arguments

Ist Teil von

• Journal of mathematical analysis and applications, 1988-11, Vol.136 (1), p.54-65

Ort / Verlag

San Diego, CA: Elsevier Inc

Erscheinungsjahr

1988

Link zum Volltext

Quelle

EZB-NALI5-00465 Elsevier Archive NL

Beschreibungen/Notizen

• New oscillation theorems for the damped differential equation x ( n) ( t) + q( t) f( x[ g( t)]) h( x ( n − 1) [ σ( t)]) = 0, n is even, and the damped forced differential equation x ( n) ( t) + q( t) f( x[ g( t)]) h( x ( n − 1) [ σ( t)]) = e( t), n is even, are established. This is done by reducing the above equations into inequalities of first order. Conditions on fh of the form ∫ ±0 du f(u) h(u) < ∞ or f(x) h(x) x α ⩾ γ > 0 for x ≠ 0 , where α is the ratio of two positive odd integers with 0 < α ⩽ 1, are required in some of our results. The function σ plays an important role as a retarded argument, while no restriction is imposed on the function g.