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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. [ABSTRACT FROM AUTHOR]

In this paper, the authors consider the existence of periodic solutions for a kind of second neutral functional differential equation as follows: in the critical case | c| = 1. By employing Mawhin's continuation theorem and some analysis techniques, some new results are obtained. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, the problem of absolute stability for general Lurie control systems with multi-nonlinear 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. [ABSTRACT FROM AUTHOR]