Abstract
In this paper, a class of fourth-order nonlinear neutral dynamic equations on time scales is investigated. We obtain some sufficient conditions for the existence of nonoscillatory solutions tending to zero with some characteristics of the equations by Krasnoselskii’s fixed point theorem. Finally, two interesting examples are presented to show the significance of the results.
Highlights
1 Introduction In this paper, we consider the existence of nonoscillatory solutions tending to zero of a fourth-order nonlinear neutral dynamic equation
2 Main results we present some sufficient conditions for the existence of eventually positive solutions of (1) under different assumptions
There exists T1 ∈ [t0, ∞)T such that (1) has two eventually positive solutions x1 and x2 tending to zero, which satisfy that R0(t, xi(t)) > 0, R1(t, xi(t)) < 0, i = 1, 2, R2(t, x1(t)) < 0, R3(t, x1(t)) < 0, R2(t, x2(t)) > 0, and R3(t, x2(t)) > 0 for t ∈ [T1, ∞)T
Summary
2 Main results we present some sufficient conditions for the existence of eventually positive solutions of (1) under different assumptions.
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