We study the existence of multiple nonnegative solutions for the doubly singular three-point boundary value problem with derivative dependent data function-(p(t)y′(t))′=q(t)f(t,y(t),p(t)y′(t)),0<t<1,y(0)=0,y(1)=α1y(η). Here,p∈C[0,1]∩C1(0,1]withp(t)>0on(0,1]andq(t)is allowed to be discontinuous att=0. The fixed point theory in a cone is applied to achieve new and more general results for existence of multiple nonnegative solutions of the problem. The results are illustrated through examples.
Abstract
As counterfeiting techniques and processes grow in sophistication, the methods needed to detect these parts must keep pace. This has the unfortunate effect of raising the costs associated with managing this risk. In order to ensure that the resources devoted to counterfeit detection are commensurate with the potential effects and likelihood of counterfeit part usage in a particular application, a risk based methodology has been adopted for testing of electrical, electronic, and electromechanical (EEE) parts by the SAE AS6171 set of standards. This paper provides an overview of the risk assessment methodology employed within AS6171 to determine the testing that should be utilized to manage the risk associated with the use of a part. A scenario is constructed as a case study to illustrate how multiple solutions exist to address the risk for a particular situation, and the choice of any specific test plan can be made on the basis of practical considerations, such as cost, time, or the availability of particular test equipment.
Multiple Solutions for Nonlinear Doubly Singular Three-Point Boundary Value Problems with Derivative Dependence
