Abstract The author of this article concerns with the existence, uniqueness, and stability weak solution to variation-inequality problem. Kirchhoff operator is a non-divergence form space variable parameter. existence generalized proved by Leray-Schauder principle parabolic regularization. uniqueness are also discussed contradiction.

The paper solves one problem by E. Prisner concerning the 2distance operator T2. This is an operator on the class Cf of all finite undirected graphs. If G is a graph from Cf , then T2(G) is the graph with the same vertex set as G in which two vertices are adjacent if and only if their distance in G is 2. E. Prisner asks whether the periodicity ≥ 3 is possible for T2. In this paper an affirmativ...

In this paper, we establish the existence and multiplicity of solutions to the following fractional Kirchhoff-type problem M(∥u∥)(−∆)u = f(x, u(x)), in Ω u = 0 in R\Ω, where N > 2s with s ∈ (0, 1), Ω is an open bounded subset of R with Lipschitz boundary, M and f are two continuous functions, and (−∆) is a fractional Laplace operator. Our main tools are based on critical point theorems and the ...

In this article, we deal with the existence of non-negative solutions class following non local problem $$ \left \{ \textstyle\begin{array}{l} \quad - M\left (\displaystyle \int _{\mathbb{R}^{n}}\int _{\mathbb{R}^{n}} \frac{|u(x)-u(y)|^{\frac{n}{s}}}{|x-y|^{2n}}~dxdy\right ) (-\Delta )^{s}_{n/s} u=\left _{\Omega }\frac{G(y,u)}{|x-y|^{\mu }}~dy \right )g(x,u) \; \text{in}\; \Omega , \\ u =0\quad...

A reconfigurable computing (RC) platform called SPACE (Seismic data Processing Accelerator with reConfigurable Engine) is proposed to accelerate the execution of 3D prestack Kirchhoff time migration (PSTM) based on the optimized 6 order NMO Correction technology (Sun et. al. 2002). Our simulations demonstrated up to 22 X performance improvement on the proposed RC platform comparing with the pur...