In the study of nonexpansive mappings and fixed point theory the domain of the mapping is usually assumed to be bounded or, as in certain approximation results (see, e.g., [20]), fixed points are assumed to exist. However in [21] Penot used uniform asymptotic concepts which he had earlier introduced in [22] to extend the Browder-Göhde-Kirk theorem to unbounded sets. The term “asymptotic” is use...

We consider the p-Laplacian problem div(a(x)|S7u\p-2Vu) + b(x)\u\p-2u = f(x, u), XGÍ2, h|öq = 0, lim u = 0, |*|-» oo where 1 < p < n , Q (C R") is an exterior domain. Under certain conditions, we show the existence of solutions for this problem via critical point theory.

It is known that abduction can be embedded into Answer Set programming (ASP). This enables sophisticated answer set solvers to be applied to abduction problems. However this approach does not scale to abduction over infinite domains, nor to unbounded abduction of individual existence, due to well-known undecidability results. The approaches to open abduction usually rely on 3-valued semantics t...

The paper is devoted to general elliptic problems in the Douglis-Nirenberg sense. We obtain a necessary and sufficient condition of normal solvability in the case of unbounded domains. Along with the ellipticity condition, proper ellipticity and Lopatinsky condition that determine normal solvability of elliptic problems in bounded domains, one more condition formulated in terms of limiting prob...

at present paper, we establish the existence of pullback $mathcal{d}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $l^2(mathbb{r}^n)times l^2(mathbb{r}^n)$. in order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{d}$-absorbing set, is pullback $widehat{d}_0$-asymptotically compact.

Various issues with regard to chaos and recurrence in infinite dimensions are discussed. The doctrine we are trying to derive is that Sobolev spaces over bounded spatial domains do host chaos and recurrence, while Sobolev spaces over unbounded spatial domains are lack of chaos and recurrence. Local Sobolev spaces over unbounded spatial domains can host chaos and are natural phase spaces e.g. fo...

Certificates of non-negativity are fundamental tools in optimization. A “certificate” is generally understood as an expression that makes the non-negativity of the function in question evident. Some classical certificates of non-negativity are Farkas Lemma and the S-lemma. The lift-and-project procedure can be seen as a certificate of non-negativity for affine functions over the union of two po...

In this note, we extend the result of [PG16] about the complexity of solving polynomial differential equations over unbounded domains to work with non-rational input. In order to deal with arbitrary input, we phrase the result in framework of Conputable Analysis [Ko91]. As a side result, we also get a uniform result about complexity of the operator, and not just about the solution. The complexi...