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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. · 0.48 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. · 0.48 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 01/2005; 21(5):10151026. · 0.48 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 01/2005; 21(6):13091314. · 0.48 Impact Factor