On $r$-neighbourly submanifolds in $\mathbb R^N$

Transcendental submanifolds of Rn

In this paper we show how the restriction of the complex algebraic cycles to real part of a complex algebraic set îs related to the real algebraic cycles of the real part As a corollary we give examples of smooth submanifolds of a Euchdean space which can not be isotoped to real parts of complex nonsingular subvaneties in the corresponding projective space Algebraic numbers are dense in R. The ...

Some results on $\mathbb{R}$-computable structures

This survey paper examines the effective model theory obtained with the BSS model of real number computation. It treats the following topics: computable ordinals, satisfaction of computable infinitary formulas, forcing as a construction technique, effective categoricity, effective topology, and relations with other models for the effective theory of uncountable structures.

Positive solutions for coupled Schrödinger system with critical exponent in RN$\mathbb{R}^{N}$ (N≥5$N\geq5$)

Existence of a ground state solution for a class of singular elliptic problem in RN$\mathbb{R}^{N}$

when p = , |f (x,u)| ≤ c(|u|+ |u|q–),  < q≤ ∗ = N N– ,N ≥ , for the corresponding results onemay refer to Brézis [], Brézis and Nirenberg [], Bartsch andWillem [] and Capozzi, Fortunato and Palmieri []. Garcia and Alonso [] generalized Brézis, Nirenberg’s existence and nonexistence results to p-Laplace equation. Moreover, let us consider the following semilinear Schrödinger equation:

Existence of nontrivial solutions for a class of biharmonic equations with singular potential in RN$\mathbb{R}^{N}$

*Correspondence: [email protected] School of Mathematics and Physics, University of South China, Hengyang, P.R. China Abstract In this paper, we study a class of biharmonic equations with a singular potential inRN . Under appropriate assumptions on the nonlinearity, we establish some existence results via the Morse theory and variational methods. We significantly extend and complement some re...