Hairong Lian

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The second order nonlinear delay differential equation with periodic coefficients x ′′(t)+ p(t)x ′(t)+ q(t)x(t) = r(t)x ′(t − τ(t))+ f (t, x(t), x(t − τ(t))), t ∈ R is considered in this work. By using Krasnoselskii’s fixed point theorem and the contraction mapping principle, we establish some criteria for the existence and uniqueness of periodic solutions(More)
and Applied Analysis 3 to BVP 1.1 when T ∞, which we call the infinite case. Some explicit examples are also given in the last section to illustrate our main results. 2. Preliminaries For the convenience of the readers, we provide here some definitions and lemmas which are important in the proof of our main results. Ge-Mawhin’s continuation theorem and the(More)
It is well known that to determine the number and distribution of the limit cycles is an open problem in the qualitative theory of planar real polynomial systems. Many researches have focused on bifurcation problems of limit cycles in the last few years, as in [Li, 2003; Han, 2012, 2013; Lloyd & Pearson, 2012; Coll et al., 2005; Xiong & Han, 2014; Yang,(More)
where T is a time scale such that 0, T ∈ T, δ,βi > 0, i = 1, . . . , m − 2, jp(s) = |s|s,p > 1,h Î Cld((0, T), (0, +∞)), and f Î C([0,+∞), (0,+∞)), 0 < ξ1 < ξ2 < · · · < ξm−2 < T ∈ T. By using several well-known fixed point theorems in a cone, the existence of at least one, two, or three positive solutions are obtained. Examples are also given in this(More)
In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t Boundary value problem of second-order differential equations on the(More)
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