In this paper, we study the existence of infinitely many solutions to the following quasilinear equation of p-Laplacian type in R (0.1) −△pu+ |u|p−2u = λV (x)|u|p−2u+ g(x, u), u ∈ W (R ) with sign-changing radially symmetric potential V (x), where 1 < p < N, λ ∈ R and △pu = div(|Du|p−2Du) is the p-Laplacian operator, g(x, u) ∈ C(R×R,R) is subcritical and p-superlinear at 0 as well as at infinit...

This paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + V(x)u=g(x, v), -triangle v - b(x)nabla v + V(x)v=f(x, u), end{array} right. $$ for $x in {R}^{N}$, where $V $, $b$ and $W$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. In this paper, we give a new technique to show the boundedness of Cerami sequences and estab...

Bioactive glass-ceramic is used as a replacement material for bone tissue due to its compatibility, bioactivity, and the ability form crystallized hydroxyapatite layer, which similar in composition structure inorganic component of mineral phase. In this paper, bioglass-ceramic was toughened using zirconia improve mechanical behaviour (i.e. crack opening dsplacement fracture toughness). The toug...

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Many modern computer applications are open distributed systems in which the (very many) constituent components are spread throughout a network, in a decentralized control regime, and which are subject to constant change throughout the system’s lifetime. Examples include the grid (Foster and Kesselman 1998), peer-to-peer computing (Gong 2002), the semantic web (BernersLee et al. 2001), web servi...

this paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + v(x)u=g(x, v), -triangle v - b(x)nabla v + v(x)v=f(x, u), end{array} right. $$ for $x in {r}^{n}$, where $v $, $b$ and $w$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. in this paper, we give a new technique to show the boundedness of cerami sequences and establi...

Nonlinear Schrödinger equations with an external magnetic field and a power nonlinearity subcritical exponent \begin{document}$ p $\end{document} are considered. It is established lower bound to the number of nontrivial solutions these in terms topology domains which problem given if id="M2">\begin{docume...