This paper is devoted to the description of the interval of parameters for which the general linear n th -order equationwith ai ∈ C n−i (I), is disconjugate on I. Such interval is characterized by the closed to zero eigenvalues of this problem coupled with (k, n − k) boundary conditions, given by u(a) = · · · = u (k−1) (a) = u(b) = · · · = u (n−k−1) (b) = 0 , 1 ≤ k ≤ n − 1 .(2)
This paper is devoted to the study of the sign of the Green's function related to a general linear nth-order operator, depending on a real parameter, T n [M], coupled with the (k, n -k) boundary value conditions.If the operator T n [M] is disconjugate for a givenM, we describe the interval of values on the real parameter M for which the Green's function has constant sign.One of the extremes of the interval is given by the first eigenvalue of the operatorThe other extreme is related to the minimum (maximum) of the first eigenvalues of (k -1, n -k + 1) and (k + 1, n -k -1) problems.Moreover, if n -k is even (odd) the Green's function cannot be nonpositive (nonnegative).To illustrate the applicability of the obtained results, we calculate the parameter intervals of constant sign Green's functions for particular operators. Our method avoids the necessity of calculating the expression of the Green's function.We finalize the paper by presenting a particular equation in which it is shown that the disconjugation hypothesis on operator T n [M] for a givenM cannot be eliminated.
The aim of this paper is to study the following fourth-order operator:coupled with the non-homogeneous simply supported beam boundary conditions:First, we prove a result which makes an equivalence between the strongly inverse positive (negative) character of this operator with the previously introduced boundary conditions and with the homogeneous boundary conditions, given by:Once that we have done that, we prove several results where the strongly inverse positive (negative) character of T [p, c] it is ensured.Finally, there are shown a couple of result which say that under the hypothesis that h > 0, we can affirm that the problem for the homogeneous boundary conditions has a unique constant sign solution.
Abstract. As the volume of global trade expands, so does the risk of alien species reaching new regions. Bombus (Bombus) terrestris (Linnaeus) (Hymenoptera: Apidae) is a bumble bee traded internationally for crop pollination and is now considered an invasive species in New Zealand, Japan, and throughout South America. We newly document its presence on Navarino Island, Cape Horn, Biosphere Reserve, Chile (55°S), the southernmost locality reached by this species to date.
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