Abstract:
We prove the existence of multiple positive solutions to singular boundary-value problems for fourth-order equations in abstract spaces. Our results improve and extend that obtained in [14,15,16], even in the scalar case.

Abstract:
This paper investigates a class of delay differential systems with feedback control. Sufficient conditions are obtained for the existence and uniqueness of the positive periodic solution by utilizing some results from the mixed monotone operator theory. Meanwhile, the dependence of the positive periodic solution on the parameter is also studied. Finally, an example together with numerical simulations is worked out to illustrate the main results.

Abstract:
By using the fixed point theorem on cone, some sufficient conditions are obtained on the existence of positive periodic solutions for a class of -species competition systems with impulses. Meanwhile, we point out that the conclusion of (Yan, 2009) is incorrect. 1. Introduction In recent years, the problem of periodic solutions of the ecological species competition systems has always been one of the active areas of research and has attracted much attention. For instance, the traditional Lotka-Volterra competition system is a rudimentary model on mathematical ecology which can be expressed as follows: Owing to its theoretical and practical significance, the systems have been studied extensively by many researchers. And many excellent results which concerned with persistence, extinction, global attractivity of periodic solutions, or almost periodic solutions have been obtained. However, the Lotka-Volterra competition systems ignore many important factors, such as the age structure of a population or the effect of toxic substances. So, more complicated competition systems are needed. In 1973, Ayala and Gilpin proposed several competition systems. One of the systems is the following competition system: where is the population density of the th species; is the intrinsic exponential growth rate of the th species; is the environmental carrying capacity of species in the absence of competition; provides a nonlinear measure of interspecific interference, provides a nonlinear measure of interspecific interference. On the other hand, in the study of species competition systems, the effect of some impulsive factors has been neglected, which exists widely in the real world. For example, the harvesting or stocking occur at fixed time, natural disaster such as fire or flood happen unexpectedly, and some species usually migrate seasonally. Consequently, such processes experience short-time rapid change which can be described by impulses. Therefore, it is important to study the existence of the periodic solutions of competitive systems with impulse perturbation (see [1–7] and the references therein). For example, by using the method of coincidence degree, Wang [1] considered the existence of periodic solutions for the following -species Gilpin-Ayala impulsive competition system: where the constant satisfied . What is more, [1] also obtained several results for the persistence and global attractivity of the periodic solution of the model. In [2], Yan applied the Krasnoselskii fixed point theorem to investigate the following n-species competition system: where the

Abstract:
Using the theory of the fixed point index in a cone and the Leray-Schauder degree, this paper investigates the existence and multiplicity of nontrivial solutions for a class of fourth order m-point boundary-value problems.

Abstract:
Using a specially constructed cone and the fixed point index theory, this paper shows the existence of multiple positive solutions for a class of nonresonant singular boundary-value problem of second-order differential equations. The nonexistence of positive solution is also studied.

Abstract:
Using a fixed point theorem due to Avery and Peterson, this article shows the existence of solutions for multi-point boundary-value problem with p-Laplace operator and parameters. Also, we present an example to illustrate the results obtained.

Abstract:
Using the well known Leggett-Williams fixed point theorem, we study the existence of periodic solutions for a class of impulsive functional equations with feedback control. The main results are illustrated with two examples.

Abstract:
By using bifurcation techniques, this paper investigates the existence of nodal solutions for a class of fourth-order -point boundary value problems. Our results improve those in the literature.

Abstract:
This paper deals with global structure of the following periodic boundary value problem of third order differential equation $u^{\prime\prime\prime}+\r^3u =\ld f(t, u)$, $0< t < 2\pi$, with $u^{(i)}(0)= u^{(i)}(2\pi)$, $i=0, 1, 2$, where $\r\in (0, \f{1}{\s})$ is a constant, $ \ld\in R^+=0, +\i)$ is a parameter, and $f$ is singular at $t=0$, $t=2\pi$ and $u=0$. Also, $f$ is sublinear at $\i$.