In this paper, a linearized asymptotic stability result for a Caputo-Katugampola fractional-order systems is described. An application is given to demonstrate the validity of the proposed results.

In this paper, we establish sufficient conditions for the existence of positive solutions for a two-point boundary value problem of a third order differential equation at resonance on the positive half line. Our results are based on the Leggett-Williams norm-type theorem of coincidence. As an application, an example is given to demonstrate our results.

In this paper, we consider a split equality fixed point problem for two quasi-asymptotically pseudocontractive mappings. Some properties for quasi-asymptotically pseudocontractive operators are presented. An iterative algorithm for solving the split common fixed point problem for two quasi-pseudocontractive operators is constructed. Weak and strong convergence theorems are established in Hilbert spaces.

A stage-structured plant-pollinator mutualism model with the Beddington-DeAngelis functional response is introduced and studied. Our results show that the mutual interference concerning pollinator k 2 does not have an impact on the permanence and the extinction of the stage-structured plant-pollinator mutualism. However, when the positive equilibrium is unstable, a sufficient large k 2 can drive the system into a globally stable. Furthermore, some sufficient cases which guarantee the permanence of the system are obtained. The local stability of the system is discussed by the sign of eigenvalue. Finally, we analyze the global stability of the system via iterative methods.

In this paper, we study the existence and uniqueness, continuous dependence on initial conditions and the boundedness of solutions for a system of impulsive differential equations using the fixed point approach in vector Banach spaces. The compactness and u.s.c. of operator solutions are also investigated.

This paper is devoted to the study of the existence of at least three non-negative classical solutions for a second-order multi-point boundary value system. We use variational methods for smooth functionals defined on reflexive Banach spaces in order to achieve our results. An example is provided to illustrate the applicability of our results.

We prove the existence of a nonnegative weak solution 0 ≡ u ∈ H 1 0 (Ω) to the singular semilinearis a Carathéodory function which satisfies some suitable hypothesis.We also obtain results about the problem with a parameter -∆u = χ {u>0} au -α + λ f (., u) in Ω, u ≥ 0 in Ω, u = 0 on ∂ Ω.