In this paper, a special class of boundary value problems, −▵u=λuq+ur,inΩ,u>0, inΩ,n·∇u+g(u)u=0,on∂Ω, where 0<q<1<r<N+2N−2 and g:[0,∞)→(0,∞) is nondecreasing C1 function. Here, Ω⊂RN(N≥3) bounded domain with smooth ∂Ω λ>0 parameter. The existence the solution verified via sub- super-solutions method. addition, influences parameters on minimum are also discussed. second positive...

This paper introduces the Pyramidal Capacitated Vehicle Routing Problem (PCVRP) as a restricted version of the Capacitated Vehicle Routing Problem (CVRP). In the PCVRP each route is required to be pyramidal in a sense generalized from the Pyramidal Traveling Salesman Problem (PTSP). A pyramidal route is defined as a route on which the vehicle first visits customers in increasing order of custom...

Let f ∈ C[−ω, ω], 0 < ω < π, be nonlinear and nondecreasing. We wish to estimate the degree of approximation of f by trigonometric polynomials that are nondecreasing in [−ω, ω]. We obtain estimates involving the second modulus of smoothness of f and show that one in general cannot have estimates with the third modulus of smoothness.

A number of optimization methods require as a rst step the construction of a dominating set (a set containing an optimal solution) enjoying properties such as compactness or convexity. In this note we address the problem of constructing dominating sets for problems whose objective is a componentwise nondecreasing function of (possibly an in nite number of) convex functions, and we show how to o...