Coloring ${\mathbb R}^n$

On the complexity of $\mathbb H$-coloring for special oriented trees

For a fixed digraph H, the H-coloring problem is the problem of deciding whether a given input digraph G admits a homomorphism to H. The CSP dichotomy conjecture of Feder and Vardi is equivalent to proving that, for any H, the H-coloring problem is in in P or NP-complete. We confirm this dichotomy for a certain class of oriented trees, which we call special trees (generalizing earlier results o...

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

$\mathbb{Z}_{q}(\mathbb{Z}_{q}+u\mathbb{Z}_{q})$-Linear Skew Constacyclic Codes

In this paper, we study skew constacyclic codes over the ring ZqR where R = Zq + uZq, q = p s for a prime p and u2 = 0. We give the definition of these codes as subsets of the ring ZqR . Some structural properties of the skew polynomial ring R[x, θ] are discussed, where θ is an automorphism of R. We describe the generator polynomials of skew constacyclic codes over R and ZqR. Using Gray images ...

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...