This paper is devoted to the limit cycle bifurcation problem for some cubic polynomial systems, whose unperturbed systems have a period annulus and two invariant lines. Using the first order Melnikov function and Chebyshev criterion, we obtain the maximum number of limit cycles bifurcating from the period annulus. It improves a known result given by Sui and Zhao [Internat. J. Bifur. Chaos Appl. Sci. Engrg. 28 (2018), 1850063].
In this paper, we present several new oscillation criteria for a second order nonlinear differential equation with mixed neutral terms of the form (r(t)(z (t)) α) + q(t)x β (σ (t)) = 0, t ≥ t 0 , where z(t) = x(t) + p 1 (t)x(τ (t)) + p 2 (t)x(λ(t)) and α, β are ratios of two positive odd integers. Our results improve and complement some well-known results which were published recently in the literature. Two examples are given to illustrate the efficiency of our results.
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