Abstract. In this paper we prove several generalizations of the Banach fixed point theorem for partial metric spaces (in the sense of O'Neill) given in [14], obtaining as a particular case of our results the Banach fixed point theorem of Matthews ([12]), and some well-known classical fixed point theorems when the partial metric is, in fact, a metric.2000 AMS Classification: 54H25, 54E50, 54E99, 68Q55.
We present new oscillation criteria for the second order forced ordinary differential equation with mixed nonlinearities:where p(t), q(t), q i (t), e(t) ∈ C[0, ∞), p(t) is positive and differentiable, α 1 > · · · > α m > 1 > α m+1 > · · · > α n . No restriction is imposed on the forcing term e(t) to be the second derivative of an oscillatory function. When n = 1, our results reduce to those of El-Sayed [M.A. El-Sayed, An oscillation criterion for a forced second order linear differential equation, Proc.
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