We consider a bistable differential-difference equation with inhomogeneous diffusion. Employing a piecewise linear nonlinearity, often referred to as McKean’s caricature of the cubic, we construct front solutions which correspond, in the case of homogeneous diffusion, to monotone traveling front solutions or stationary front solutions in the case of propagation failure. A general form for these...

In this paper we prove the existence of positive solutions for the three-point singular boundary-value problem −[φp(u)] = q(t)f(t, u(t)), 0 < t < 1 subject to u(0)− g(u′(0)) = 0, u(1)− βu(η) = 0 or to u(0)− αu(η) = 0, u(1) + g(u′(1)) = 0, where φp is the p-Laplacian operator, 0 < η < 1; 0 < α, β < 1 are fixed points and g is a monotone continuous function defined on the real line R with g(0) = ...

We consider the design and analysis of numerical methods for approximating positive solutions to nonlinear geometric elliptic partial differential equations containing critical exponents. This class of problems includes the Yamabe problem and the Einstein constraint equations, which simultaneously contain several challenging features: high spatial dimension n > 3, varying (potentially non-smoot...

In this note, small amplitude free vibration of a double-beam system in presence of inner layer nonlinearity is investigated. The nonlinearity is due to inner layer material and is not related to large amplitude vibration. At first, frequencies of a double-beam system with linear inner layer are studied and categorized as synchronous and asynchronous frequencies. It is revealed that the inner l...

where λ is a positive parameter. The nonlinearity f(u) is called semipositone if f(0) < 0. In this paper we will only consider the positive solutions of (1.1). Semipositone problems were introduced by Castro and Shivaji in [CS1], and they arise from various disciplines, like astrophysics and population dynamics. (see [CMS] for more details.) It is possible that (1.1) has non-negative solutions ...

Integral nonlinearity (INL) should be main source of ADC's harmonic distortion. The basic question is importance of dynamic INL. There are still open questions how to describe dynamic INL and if the dynamic corrections of ADC have sense. Key-Words: ADC, testing, static, dynamic, INL, hysteresis

We use a monotone iterative method in the presence of lower and upper solutions to discuss the existence and uniqueness of mild solutions for the initial value problem u′(t) + Au(t) = f(t, u(t), Tu(t)), t ∈ J, t 6= tk, ∆u|t=tk = Ik(u(tk)), k = 1, 2, . . . , m, u(0) = x0, where A : D(A) ⊂ E → E is a closed linear operator and −A generates a strongly continuous semigroup T (t)(t ≥ 0) in E. Under ...

This paper provides less conservative stability conditions for bilateral teleoperation by exploiting the advantages of the integral quadratic constraint (IQC) framework, where the environment can be defined as a memoryless, bounded, and monotonic nonlinear operator. Recent advances in multiplier theory for appropriate classes of uncertainties/nonlinearities are applied. Since the classes of mul...

Measurement of integral non-linearity (INL) and differential non-linearity (DNL) of an A/D converter using the histogram method incurs large test time. This test time can be a significant percentage of the total test time, especially for high resolution and low sampling-speed A/D converters. This paper describes a test methodology for measuring the INL and DNL specifications of A/D converters b...