The aim of this paper is investigating the existence one or more weak solutions coupled quasilinear elliptic system gradient type \[ (P)\qquad \left\{ \begin{array}{ll} - {\rm div} (A(x, u)\vert\nabla u\vert^{p_1 -2} \nabla u) + \frac{1}{p_1}A_u (x, u\vert^{p_1} = G_u(x, u, v) &\hbox{ in $\Omega$,}\\[5pt] (B(x, v)\vert\nabla v\vert^{p_2 +\frac{1}{p_2}B_v(x, v\vert^{p_2} G_v\left(x, v\right) u v...

Adopting various unified equations of state (EOSs), we examine the quasinormal modes gravitational waves from cold neutron stars. We focus on fundamental ($f$-), 1st pressure ($p_1$-), and spacetime ($w_1$-) modes, derive empirical formulae for frequencies damping rate those modes. With resultant formulae, find that value $\eta$, which is a specific combination nuclear saturation parameters, ca...

We consider the natural time-dependent fractional p-Laplacian equation posed in whole Euclidean space, with parameter $$12$$ has been dealt recen...

We prove the existence of critical points vortex type Hamiltonians \[ H(p_1,\ldots, p_N) = \sum_{{i,j=1}\atop{i\ne j}} ^N \Gamma_i\Gamma_jG(p_i,p_j)+\Psi(p_1,\dots,p_N) \] on a closed Riemannian surface $(\Sigma,g)$ which is not homeomorphic to sphere or projective plane. Here $G$ denotes Green function Laplace-Beltrami operator in $\Sigma$, $\Psi\colon \Sigma^N\to\mathbb{R}$ may be any class $...

We study bilinear rough singular integral operators $$\mathcal {L}_{\Omega }$$ associated with a function $$\Omega $$ on the sphere $$\mathbb {S}^{2n-1}$$ . In recent work of Grafakos et al. (Math Ann 376:431–455, 2020), they showed that is bounded from $$L^2\times L^2$$ to $$L^1$$ , provided \in L^q(\mathbb {S}^{2n-1})$$ for $$4/3<q\le \infty mean value zero. this paper, we provide generalizat...

We establish $L^{p_1}\times\cdots\times L^{p_k}\to L^r$ and $\ell^{p_1}\times\cdots\times \ell^{p_k}\to \ell^r$ type bounds for multilinear maximal operators associated to averages over isometric copies of a given non-degenerate $k$-simplex in both the continuous discrete settings. These provide natural extensions $L^p\to L^p$ $\ell^p\to \ell^p$ Stein's spherical operator operator, with each th...

In this article, we provide a multilinear version of the Hörmander multiplier theorem with Lorentz–Sobolev space condition. The work is motivated by recent result first author and Slavíková [12] where an analogous classical was obtained; sharp in many ways reduces number indices that appear statement theorem. As natural extension linear case, work, prove if $$mn/2<s<mn$$ , then $$\begin{aligned...

Abstract We prove that, for almost all $r \leq N^{1/2}/\log^{O(1)}N$, any given $b_1 \ (\mathrm{mod}\ r)$ with $(b_1, r) = 1$, and $b_2 $(b_2, we have that natural numbers $2n N$ \equiv b_1 + b_2 can be written as the sum of two prime p_1 p_2$, where $p_1 $p_2 r)$. This improves previous result which required N^{1/3}/\log^{O(1)}N$ instead N^{1/2}/\log^{O(1)}N$. also improve some other results c...