Positive Solutions of Volterra Integro–differential Equations
نویسنده
چکیده
We present some sufficient conditions such that Eq. (1) only has solutions with zero points in (0,∞). Moreover, we also obtain some conditions such that Eq. (1) has a positive solution on [0,+∞). The motivation of this work comes from the work of Ladas, Philos and Sficas [5]. They discussed the oscillation behavior of Eq. (1) when P (t, s) = P (t− s) and g(t) = t. They obtained a necessary and sufficient condition under which every solution of the equation is positive on [0,+∞). Note that Eq. (1) is not a generalization of the equation in [5] because of the condition g(t) < t, which we require here. From (2), we see that the function g is nondecreasing and g(0) = 0, so, Eq. (1) has a lag with a finite fixed point t = 0. Karakostas [4] has studied linear delay differential equations with delays having fixed point and obtained that solutions
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