This paper studies the boundedness, global asymptotic stability, and periodicity of positive solutions of the equation xn f xn−2 /g xn−1 , n ∈ N0, where f, g ∈ C 0,∞ , 0,∞ . It is shown that if f and g are nondecreasing, then for every solution of the equation the subsequences {x2n} and {x2n−1} are eventually monotone. For the case when f x α βx and g satisfies the conditions g 0 1, g is nondec...

and Applied Analysis 3 an energy condition. Section 4 is devoted to long time behaviors of global solutions, including the existence of global fast solution and slow solution. 2. Local Existence and Uniqueness In this section, we prove the following local existence and uniqueness of the solution to 1.2 by contraction mapping principle. Theorem 2.1. For any given u0 satisfying u0 ∈ C1 α 0, s0 wi...

and Applied Analysis 3 is called the auxiliary equation of the Euler differential equation 2.1 , and every solution of 2.1 is of the form yh x ⎧ ⎪⎨ ⎪⎩ c1x m1 c2x2 if m1 and m2 are distinct roots of 2.2 , c1 c2 lnx x 1−α /2 if 1 − α 2 is a double root of 2.2 , 2.3 where c1 and c2 are complex constants see 21, Section 2.7 . Theorem 2.1. Let α and β be complex constants such that no root of the au...

We consider the heat equation ∂ty − div(c∇y) = H with a discontinuous coefficient in three connected situations. We give uniqueness and stability results for the diffusion coefficient c(·) in the main case from measurements of the solution on an arbitrary part of the boundary and at a fixed time in the whole spatial domain. The diffusion coefficient is assumed to be discontinuous across an unkn...

The thermal requirements for development of Dermanyssus gallinae were studied under laboratory conditions at 15, 20, 25, 30 and 35 degrees C, a 12h photoperiod and 60-85% RH. The thermal requirements for D. gallinae were as follows. Preoviposition: base temperature 3.4 degrees C, thermal constant (k) 562.85 degree-hours, determination coefficient (R(2)) 0.59, regression equation: Y= -0.006035 +...

Abstract: We analytically calculate higher order corrections to coefficient functions of the operator product expansion (OPE) for the Euclidean correlator of two energy-momentum tensors in massless QCD. These are the three-loop contribution to the coefficient C0 in front of the unity operator O0 = 1 and the one and two-loop contributions to the coefficient C1 in front of the gluon “condensate” ...