FORCED OSCILLATION OF SECOND ORDER DIFFERENTIAL EQUATIONS WITH MIXED NONLINEARITIES

doi:10.1016/S0252-9602(11)60261-0

Abstract

Abstract:

This article is concerned with the oscillation of the forced second order differential equation with mixed nonlinearities

(a(t)( x´(t)^γ)´+p₀(t) x^γ( g₀(t))+∑_i=1ⁿp_i(t)l x(g_i(t))|^αisgn x (g_i(t)) =e(t),
where γ is a quotient of odd positive integers, α_i>0, i=1, 2, …, n, a, e, and p_i∈C([ 0, ∞) , {R}, α(t) >0, g_i: R→R are positive continuous functions on R with lim_t→∞g_i(t)=∞, i=0, 1, …, n. Our results generalize and improve the results in a recent article by Sun and Wong [29].

Key words: Oscillation, functional differentail equations, second order

CLC Number:

34C10

Taher S.Hassan, Lynn Erbe, Allan Peterson. FORCED OSCILLATION OF SECOND ORDER DIFFERENTIAL EQUATIONS WITH MIXED NONLINEARITIES[J].Acta mathematica scientia,Series B, 2011, 31(2): 613-626.

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