In this paper, we discuss nonlinear fractional difference equations with the Caputo like difference operator. Some asymptotic stability results of equations under investigated are obtained by employing Schauder fixed point theorem and discrete Arzela-Ascoli’s theorem. Three examples are also provided to illustrate our main results.

We study the existence and stability of periodic solutions of a canonical mass-spring model of electrostatically actuated micro-electro-mechanical system (MEMS) by means of classical topological techniques like a-priori bounds, Leray-Schauder degree and topological index. A saddle-node bifurcation is revealed, in analogy with the autonomous case.

This paper deals with the existence of positive solutions for a boundary value problem involving a nonlinear functional differential equation of fractional order α given by Dαu(t) + f(t, ut) = 0, t ∈ (0, 1), 2 < α ≤ 3, u′(0) = 0, u′(1) = bu′(η), u0 = φ. Our results are based on the nonlinear alternative of Leray-Schauder type and Krasnosel’skii fixed point theorem.

Existence of traveling wave fronts for delayed lattice differential equations is established by Schauder fixed point theorem. The main result is applied to a delayed and discretely diffusive model for the population of Daphnia magna.  2004 Elsevier Inc. All rights reserved.

In this article we obtain some positive results about the existence of a common nontrivial invariant subspace for N-tuples of not necessarily commuting operators on Banach spaces with a Schauder basis. The concept of joint quasinilpotence plays a basic role. Our results complement recent work by Kosiek [6] and Ptak [8].

in this paper, we study a coupled system of nonlinear fractional differential equations with multi-point boundary condi- tions. the differential operator is taken in the riemann-liouville sense. applying the schauder fixed-point theorem and the contrac- tion mapping principle, two existence results are obtained for the following system d^{alpha}_{0+}x(t)=fleft(t,y(t),d^{p}_{0+}y(t)right), t in (0,...

A generalization of the classical Leray-Schauder fixed point theorem, based on the infinitedimensional Borsuk-Ulam type antipode construction, is proposed. Two completely different proofs based on the projection operator approach and on a weak version of the well known Krein-Milman theorem are presented. MIRAMARE – TRIESTE May 2007 [email protected]; [email protected]

In this paper we investigate the existence of solutions of a class of four-point boundary value problems for a fourth order ordinary differential equation. Our analysis relies on a nonlinear alternative of Leray–Schauder type. c © 2007 Elsevier Ltd. All rights reserved.

We consider a strongly coupled reactiondiffusion system describing three interacting species in a simple food chain structure. Based on the Leray-Schauder degree theory, the existence of non-constant positive steady states is investigated. The results indicate that, when the intrinsic growth rate of the middle species is small, crossdiffusions of the predators versus the preys are helpful to cr...

In this paper, we give some sufficient conditions under which perturbations preserve Hilbert frames and near-Riesz bases. Similar results are also extended to frame sequences, Riesz sequences and Schauder frames. It is worth mentioning that some of our perturbation conditions are quite different from those used in the previous literature on this topic.