We study a nonlinear nonhomogeneous Dirichlet problem with nonsmooth potential which is superlinear but without satisfying the Ambrosetti-Rabinowitz condition. Using critical point theory and groups we prove two multiplicity theorems producing three five solutions respectively. In second theorem, provide sign information for all are ordered.

Quantum search/amplitude amplification algorithms are designed to be able to amplify the amplitude in the target state linearly with the number of operations. Since the probability is the square of the amplitude, this results in the success probability rising quadratically with the number of operations. This paper presents a new kind of quantum search algorithm in which the amplitude of the tar...

We show that an interior-point method for monotone variational inequalities exhibits superlinear convergence provided that all the standard assumptions hold except for the well-known assumption that the Jacobian of the active constraints has full rank at the solution. We show that superlinear convergence occurs even when the constant-rank condition on the Jacobian assumed in an earlier work doe...

We consider the convergence properties of return algorithms for a large class of rate-independent plasticity models. Based on recent results for semismooth functions, we can analyze these algorithms in the context of semismooth Newton methods guaranteeing local superlinear convergence. This recovers results for classical models but also extends to general hardening laws, multi-yield plasticity,...

Sensory hair cell ribbon synapses respond to graded stimulation in a linear, indefatigable manner, requiring that vesicle trafficking to synapses be rapid and nonrate-limiting. Real-time monitoring of vesicle fusion identified two release components. The first was saturable with both release rate and magnitude varying linearly with Ca(2+), however the magnitude was too small to account for sust...

We present an algorithm that achieves superlinear convergence for nonlinear programs satisfying the Mangasarian-Fromovitz constraint qualiication and the quadratic growth condition. This convergence result is obtained despite the potential lack of a locally convex augmented Lagrangian. The algorithm solves a succession of subproblems that have quadratic objective and quadratic constraints, both...

The superlinear convergence of the preconditioned CGM is studied for nonsymmetric elliptic problems (convection-diffusion equations) with mixed boundary conditions. A mesh independent rate of superlinear convergence is given when symmetric part preconditioning is applied to the FEM discretizations of the BVP. This is the extension of a similar result of the author for Dirichlet problems. The di...

In this paper we use the method of upper and lower solutions combined with degree theoretic techniques to prove the existence of multiple positive solutions to semipositone superlinear systems of the form −∆u = g1(x, u, v) −∆v = g2(x, u, v) on a smooth, bounded domain Ω ⊂ R with Dirichlet boundary conditions, under suitable conditions on g1 and g2. Our techniques apply generally to subcritical,...

In our paper, we present a sparse quasi-Newton method, called the direct Broyden for solving nonlinear equations. The method can be seen as Broyden-like and is least change update satisfying sparsity condition tangent simultaneously. local q-superlinear convergence presented based on bounded deterioration property Dennis–Moré condition. By adopting nonmonotone line search, establish global supe...