Search results for "Nonlinear system"

Classification and non-existence results for weak solutions to quasilinear elliptic equations with Neumann or Robin boundary conditions

2021

Abstract We classify positive solutions to a class of quasilinear equations with Neumann or Robin boundary conditions in convex domains. Our main tool is an integral formula involving the trace of some relevant quantities for the problem. Under a suitable condition on the nonlinearity, a relevant consequence of our results is that we can extend to weak solutions a celebrated result obtained for stable solutions by Casten and Holland and by Matano.

Existence of viscosity solutions to two-phase problems for fully nonlinear equations with distributed sources

2018

In this paper we construct a viscosity solution of a two-phase free boundary problem for a class of fully nonlinear equation with distributed sources, via an adaptation of the Perron method. Our results extend those in [Caffarelli, 1988], [Wang, 2003] for the homogeneous case, and of [De Silva, Ferrari, Salsa, 2015] for divergence form operators with right hand side.

Active spike transmission in the neuron model with a winding threshold manifold

2012

International audience; We analyze spiking responses of excitable neuron model with a winding threshold manifold on a pulse stimulation. The model is stimulated with external pulse stimuli and can generate nonlinear integrate-and-fire and resonant responses typical for excitable neuronal cells (all-or-none). In addition we show that for certain parameter range there is a possibility to trigger a spiking sequence with a finite number of spikes (a spiking message) in the response on a short stimulus pulse. So active transformation of N incoming pulses to M (with M>N) outgoing spikes is possible. At the level of single neuron computations such property can provide an active "spike source" comp…

Blow-up collocation solutions of nonlinear homogeneous Volterra integral equations

2011

In this paper, collocation methods are used for detecting blow-up solutions of nonlinear homogeneous Volterra-Hammerstein integral equations. To do this, we introduce the concept of "blow-up collocation solution" and analyze numerically some blow-up time estimates using collocation methods in particular examples where previous results about existence and uniqueness can be applied. Finally, we discuss the relationships between necessary conditions for blow-up of collocation solutions and exact solutions.

A non-linear Bishop–Phelps–BollobÁs type theorem

2018

Doubly nonlinear equations with unbounded operators

2004

Abstract The solvability of the evolution system v′(t)+ B (t)u(t)∋ f (t),v(t)∈ A (t)u(t) , 0 A (t) are bounded, possibly degenerate, subdifferentials and B (t) are unbounded subdifferentials.

A Criterion for Attaining the Welch Bounds with Applications for Mutually Unbiased Bases

2008

The paper gives a short introduction to mutually unbiased bases and the Welch bounds and demonstrates that the latter is a good technical tool to explore the former. In particular, a criterion for a system of vectors to satisfy the Welch bounds with equality is given and applied for the case of MUBs. This yields a necessary and sufficient condition on a set of orthonormal bases to form a complete system of MUBs. This condition takes an especially elegant form in the case of homogeneous systems of MUBs. We express some known constructions of MUBs in this form. Also it is shown how recently obtained results binding MUBs and some combinatorial structures (such as perfect nonlinear functions an…

Nonlinear Nonhomogeneous Robin Problems with Almost Critical and Partially Concave Reaction

2020

We consider a nonlinear Robin problem driven by a nonhomogeneous differential operator, with reaction which exhibits the competition of two Caratheodory terms. One is parametric, $$(p-1)$$-sublinear with a partially concave nonlinearity near zero. The other is $$(p-1)$$-superlinear and has almost critical growth. Exploiting the special geometry of the problem, we prove a bifurcation-type result, describing the changes in the set of positive solutions as the parameter $$\lambda >0$$ varies.

Digital information receiver based on stochastic resonance

2003

International audience; An electronic receiver based on stochastic resonance is presented to rescue subthreshold modulated digital data. In real experiment, it is shown that a complete data restoration is achieved for both uniform and Gaussian white noise.

Approximation of piecewise smooth functions and images by edge-adapted (ENO-EA) nonlinear multiresolution techniques

2008

Abstract This paper introduces and analyzes new approximation procedures for bivariate functions. These procedures are based on an edge-adapted nonlinear reconstruction technique which is an intrinsically two-dimensional extension of the essentially non-oscillatory and subcell resolution techniques introduced in the one-dimensional setting by Harten and Osher. Edge-adapted reconstructions are tailored to piecewise smooth functions with geometrically smooth edge discontinuities, and are therefore attractive for applications such as image compression and shock computations. The local approximation order is investigated both in L p and in the Hausdorff distance between graphs. In particular, i…