Positive Solutions and Extremal Points for Differential Equations

Extremal point properties are examined for the boundary value problem x⁽ⁿ⁾ + ? ^n-2 _i=0 A_i(t)x⁽ⁱ⁾ = 0, x⁽ⁱ⁾(0) = x^(n-2)(T) = 0, 0?i?n-2, where the A_i's, a characterization for the first extremal point is given in terms of the existence of a solution which is positive with respect to a cone in a Banach space. Also, an existence theorem is obtained for a related nonlinear problem     

Extrapolation spaces and controllability of impulsive semilinear functional differential inclusions with infinite delay in Fréchet spaces

In this article, we investigate some classes of semilinear impulsive functional differential inclusions with infinite delay. It is assumed that the linear part is possibly neither densely defined nor it satisfies the Hille–Yosida condition on a Banach space, namely the extrapolated space. Our approach is based on the theory of extrapolation spaces combined with a recent Frigon nonlinear alternative for multivalued admissible contractions in Fréchet spaces.     

Existence of Three Positive Pseudo-symmetric Solutions for a One Dimensional Discrete p-Laplacian

We apply the Five Functionals Fixed Point Theorem to verify the existence of at least three positive pseudo-symmetric solutions for the discrete three point boundary value problem, ?(g(?u(t-1)))+a(t))f(u(t))=0, for t∈{a+1,…,b+1} and u(a)=0 with u(v)=u(b+2) where g(v)=|v| ^p-2 v, p>1, for some fixed v∈{a+1,…,b+1} and σ=(b+2+v)/2 is an integer.     

Inequalities based on a generalization of concavity

The concept of concavity is generalized to functions, , satisfying order differential inequalities, , and homogeneous two-point boundary conditions, , for some . A piecewise polynomial, which bounds the function, , below, is constructed, and then is employed to obtain that , where max and denotes the supremum norm. An analogous inequality for a related Green's function is also obtained. These inequalities are useful in applications of certain cone theoretic fixed point theorems.

     

Quantification of atrazine and its metabolites in urine by on-line solid-phase extraction–high-performance liquid chromatography–tandem mass spectrometry

We have developed a method using on-line solid-phase extraction–high-performance liquid chromatography–tandem mass spectrometry (SPE-HPLC-MS/MS) and isotope dilution quantification to measure atrazine and seven atrazine metabolites in urine. The metabolites measured were hydroxyatrazine, diaminochloroatrazine, desisopropylatrazine, desethylatrazine, desethylatrazine mercapturate, atrazine mercaturate and atrazine itself. Our method has good precision (relative standard deviations ranging from 4 to 20% at 5, 10 and 50 ng/mL), extraction efficiencies of 67 to 102% at 5 and 25 ng/mL, relative recoveries of 87 to 112% at 5, 25, 50 and 100 ng/mL limits of detection (LOD) ranging from 0.03 to 2.80 ng/mL. The linear range of our method spans from the analyte LOD to 100 ng/mL (40 ng/mL for atrazine and atrazine mercapturate) with R ² values of greater than 0.999 and errors about the slope of less than 3%. Our method is rapid, cost-effective and suitable for large-scale sample analyses and is easily adaptable to other biological matrices. More importantly, this method will allow us to better assess human exposure to atrazine-related chemicals. Figure A schematic representation showing the elution of the analytes from the solid-phase extraction cartridge onto the analytical column for chromatographic separation prior to MS/MS analysis     

Uniqueness implies existence and uniqueness criterion for nonlocal boundary value problems for third order differential equations

For the third order differential equation, we consider uniqueness implies existence results for solutions satisfying the nonlocal -point boundary conditions, Uniqueness of solutions of such boundary value problems is intimately related to solutions of the third order equation satisfying certain nonlocal -point boundary conditions. These relationships are investigated as well.