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ABSTRACT: In this paper, we generalize the fixed point theorem of cone expansion and compression of norm type to the theorem of functional
type. As an application, the existence of positive solutions for some fourth–order beam equation boundary value problems is
obtained. The emphasis is put on that the nonlinear term is dependent on all lower order derivatives. Acta Mathematica Sinica 01/2006; 22(6):18251830. · 0.42 Impact Factor

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ABSTRACT: The main aim of this paper is to use the continuation theorem of coincidence degree theory
for studying the existence of periodic solutions to a kind of neutral functional differential equation as
follows:
$$
{\left( {x{\left( t \right)}  {\sum\limits_{i = 1}^n {c_{i} x{\left( {t  r_{i} } \right)}} }} \right)}^{{\prime \prime }} = f{\left( {x{\left( t \right)}} \right)}{x}\ifmmode{'}\else$'$\fi{\left( t \right)} + g{\left( {x{\left( {t  \tau } \right)}} \right)} + p{\left( t \right)}.
$$
In order to do so, we analyze the structure of the linear difference operator A : C
2π →C
2π,
$$
{\left[ {Ax} \right]}{\left( t \right)} = x{\left( t \right)}  {\sum\nolimits_{i = 1}^n {c_{i} x{\left( {t  r_{i} } \right)}} }
$$
to determine some fundamental properties first, which we are going to use
throughout this paper. Meanwhile, we also prove some new inequalities which are useful for estimating
a priori bounds of periodic solutions. Acta Mathematica Sinica 12/2005; 21(6):13091314. · 0.42 Impact Factor

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ABSTRACT: By the use of continuation theorems and the duality principle it’s proved that for both
homogeneous and nonhomogeneous Sturm–Liouville boundary value problems with Laplacian type
operators, relative superlinearity implies the existence of infinitely many solutions under a few weakly
added conditions. Acta Mathematica Sinica 10/2005; 21(5):10151026. · 0.42 Impact Factor

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ABSTRACT: By means of the continuation theorem of coincidence degree theory, some new results
on the non–existence, existence and unique existence of periodic solutions for a kind of second order
neutral functional differential equation are obtained. Acta Mathematica Sinica 01/2005; 21(2):381392. · 0.42 Impact Factor

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ABSTRACT: By employing the continuation theorem of coincidence degree principle developed by Mawhin, a kind of second order pLaplacian differential equation with a deviating argument (φ p (y ' (t))) ' +f(y ' (t))+g(y(tτ(t)))=e(t) is studied. Some new results on the existence of periodic solutions are obtained. Acta Mathematica Sinica. 01/2005; 48(5).

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ABSTRACT: In this paper, using some analysis techniques and the continuation theorem of coincidence degree theory, the authors study a kind of nspecies LotkaVolterra population model with multiple deviating arguments. Some new results on the existence of positive periodic solutions are obtained. For the comparison, the model subject to this paper is more general, which includes some known LotkaVolterra type systems, such as competitive systems, predatorprey systems and so on. Meanwhile, the method to estimate a priori bounds of periodic solutions is different from the corresponding ones found in the existing literature. Acta Mathematica Sinica. 01/2005; 48(3).

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ABSTRACT: Using the method of upper and lower solutions, this paper establishes the existence of positive solutions for singular secondorder boundary value problems of the form (py ' ) ' +p(t)q(t)f(t,y,py ' )=0,0<t<1, where f(t,y,z) is singular at y=0 and z=0. Acta Mathematica Sinica. 01/2003; 46(5).

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ABSTRACT: By using the coincidence degree principle, the authors study periodic solutions for the secondorder ndimensional neutral differential system d 2 dt 2 (x(t)Cx(tτ ¯))+d dtgradF(x(t))+gradG(x(tτ(t)))=p(t)· Some sufficient conditions are obtained to guarantee the existence of periodic solutions. Acta Mathematica Sinica. 01/2003; 46(3).

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ABSTRACT: This paper uses the method of upper and lower solutions and the monotone iterative technique to investigate the existence
of maximal and minimal solutions of the periodic boundary value problem for first order impulsive functional differential
equations. Acta Mathematica Sinica 01/2002; 18(2):253262. · 0.42 Impact Factor

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ABSTRACT: Based on the concept of absolute stability, new necessary and sufficient conditions for the absolute stability of general Lurie direct control systems with multiple nonlinearities are obtained, along with some practical sufficient conditions. A numerical example illustrates the effectiveness of the results. Acta Mathematica Sinica. 01/2002; 45(2).

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ABSTRACT: In this paper, the problem of absolute stability for general Lurie control systems with multinonlinear feedback terms is
investigated. From the Lyapunov function approach, new necessary and sufficient conditions and some practical sufficient conditions
of absolute stability are derived, which improve the absolute stability for the set. A numerical example illustrates the effectiveness
of the proposed results. Acta Mathematica Sinica 10/2001; 17(4):649656. · 0.42 Impact Factor