By using the fixed-point index theory and Leggett-Williams fixed-point theorem,we study the existence of multiple solutions to the three-point boundary value problem u′′′ t a t f t, u t , u′ t 0, 0 < t < 1; u 0 u′ 0 0; u′ 1 − αu′ η λ, where η ∈ 0, 1/2 , α ∈ 1/2η, 1/η are constants, λ ∈ 0,∞ is a parameter, and a, f are given functions. New existence theorems are obtained, which extend and comple...

We study a boundary-value quasilinear elliptic problem on a generic time scale. Making use of the fixed-point index theory, sufficient conditions are given to obtain existence, multiplicity, and infinite solvability of positive solutions. AMS Subject Classification: 34B18, 39A10, 93C70.

Current generation geospatial applications primarily rely on location representations that were developed for the manipulation and display of planar maps of portions of the earth’s surface. The next generation of digital earth applications will require fundamentally new technological approaches to location representation. Improvements in the efficiency of the representation of vector location c...

‎We obtain the asymptotic expansion of the sequence with general term $frac{A_n}{G_n}$‎, ‎where $A_n$ and $G_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$‎, ‎with $d(n)$ denoting the number of positive divisors of $n$‎. ‎Also‎, ‎we obtain some explicit bounds concerning $G_n$ and $frac{A_n}{G_n}$.