A new family of minimal spectrally arbitrary patterns is presented which allow for arbitrary spectrum by using the Nilpotent-Jacobian method introduced in [J.H. Drew, C.R. Johnson, D.D. Olesky, and P. van den Driessche. Spectrally arbitrary patterns.Lin. Alg. and Appl. 308:121137, 2000]. The novel approach here is the use of the Intermediate Value Theorem to avoid finding an explicit nilpotent ...

In this paper, an impulsive boundary value problem on the half-line is considered and existence of solutions is proved using Minimization Principal and Mountain Pass Theorem.

We establish improved mean value estimates associated with the number of integer solutions certain systems diagonal equations, in some instances attaining sharpest conjectured conclusions. This is first occasion on which bounds this quali

in this paper, we prove the existence of the solution for boundary value prob-lem(bvp) of fractional dierential equations of order q 2 (2; 3]. the kras-noselskii's xed point theorem is applied to establish the results. in addition,we give an detailed example to demonstrate the main result.

in this work, by employing the krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime...

abstract.   the sturm-liouville boundary value problem of the multi-order fractional differential equation  is studied. results on the existence of solutions are established. the analysis relies on a weighted function space and a fixed point theorem. an example is given to illustrate the efficiency of the main theorems.

Sturm’s famous theorem provides an elegant algorithm to count and locate the real roots of any given real polynomial. It is less widely known that Cauchy extended this to an algebraic method to count and locate the complex roots of any given complex polynomial. We give an algebraic proof of this beautiful result, starting from the mere axioms of the fields R and C, without any further appeal to...

Abstract A deductive system is said to be structurally complete if its admissible rules are derivable. In addition, it called hereditarily all extensions complete. Citkin (1978) proved that an intermediate logic and only the variety of Heyting algebras associated with omits five finite algebras. Despite importance in theory rules, a direct proof Citkin’s theorem not widely accessible. this pape...