Positive solutions of complementary Lidstone boundary value problems

We consider the following complementary Lidstone boundary value problem (−1)my (2m+1)(t) = F(t, y(t), y′ (t)), t ∈ [0, 1] y(0) = 0, y(2k−1)(0) = y (2k−1)(1) = 0, 1 ≤ k ≤ m. The nonlinear term F depends on y ′ and this derivative dependence is seldom investigated in the literature. Using a variety of fixed point theorems, we establish the existence of one or more positive solutions for the boundary value problem. Examples are also included to illustrate the results obtained.Published versio

Existence of solutions for fourth order three-point boundary value problems on a half-line

WOS: 000365262600001In this paper, we apply Schauder's fixed point theorem, the upper and lower solution method, and topological degree theory to establish the existence of unbounded solutions for the following fourth order three-point boundary value problem on a half-line x''''(t) + q(t) f(t, x(t), x'(t), x ''(t), x'''(t)) = 0, t is an element of (0, +infinity), x ''(0) = A, x(eta) = B-1, x'(eta) = B-2, x'''(+infinity) = C, where eta is an element of (0, +infinity), but fixed, and f : [0, +infinity) x R-4 -> R satisfies Nagumo's condition. We present easily verifiable sufficient conditions for the existence of at least one solution, and at least three solutions of this problem. We also give two examples to illustrate the importance of our results.Scientific and Technological Research Council of Turkey (TUBITAK)Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK)This work was done when the first author was on academic leave, visiting Texas A&M University-Kingsville, Department of Mathematics. He gratefully acknowledges the financial support of The Scientific and Technological Research Council of Turkey (TUBITAK)

ABC: A Simple Explicit Congestion Controller for Wireless Networks

We propose Accel-Brake Control (ABC), a simple and deployable explicit congestion control protocol for network paths with time-varying wireless links. ABC routers mark each packet with an "accelerate" or "brake", which causes senders to slightly increase or decrease their congestion windows. Routers use this feedback to quickly guide senders towards a desired target rate. ABC requires no changes to header formats or user devices, but achieves better performance than XCP. ABC is also incrementally deployable; it operates correctly when the bottleneck is a non-ABC router, and can coexist with non-ABC traffic sharing the same bottleneck link. We evaluate ABC using a Wi-Fi implementation and trace-driven emulation of cellular links. ABC achieves 30-40% higher throughput than Cubic+Codel for similar delays, and 2.2X lower delays than BBR on a Wi-Fi path. On cellular network paths, ABC achieves 50% higher throughput than Cubic+Codel