Murugadass, S.

Pinelas, Sandra

Thandapani, Ethiraju

English

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FUNCTIONALDIFFERENTIALEQUATIONSVOLUME 172010, NO 1–2PP. 1–10OSCILLATION CRITERIA FOR SECOND ORDERNONLINEAR DIFFERENTIAL EQUATIONS WITHDAMPING AND MIXED NONLINEARITIESE. THANDAPANI∗, S. MURUGADASS,† AND SANDRA PINELAS‡Abstract. In this paper we present some oscillation criteria for the second orderdifferential equation of the form(r(t)x′(t))′ + p(t)x′(t) + q(t)x(t) +n∑j=1qj(t)|xαj (t)| sgn x(t) = e(t), t ≥ 0where r(t) ∈ C1[0,∞), p(t), q(t), qj(t), e(t) ∈ C[0,∞), r(t) > 0, α1 > . . . > αm > 1 >αm+1 > . . . > αn > 0(n > m ≥ 1) without assuming that p(t), q(t), qj(t) and e(t) arenonnegative. In particular, for n = 1, we obtain some new oscillation criteria. The resultsobtained in this paper extend and improve some of the existing results.AMS(MOS) subject classification. 34C10, 34C15Key Words. Nonlinear differential equation, damping term, mixed nonlinearities,second order, oscillation.1. Introduction. Consider the following second order differentialequation of the form(1.1) (r(t)x′(t))′+p(t)x′(t)+q(t)x(t)+n∑j=1qj(t)|xαj(t)| sgn x(t) = e(t), t ≥ 0∗ Ramanujan Institute for Advanced Study in Mathematics, University of Madras,Chennai - 600005, India. e-mail: ethandapani@yahoo.co.in† Ramanujan Institute for Advanced Study in Mathematics, University of Madras,Chennai - 600005, India. e-mail: murugadasssm@gmail.com‡ Departamento de Matemtica, Universidade dos Aores, Portugal. e-mail: san-dra.pinelas@clix.pt1

Oscillations criteria for second order nonlinear differential equations with damping and mixed nonlinearities

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Oscillations criteria for second order nonlinear differential equations with damping and mixed nonlinearities

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