Well-posedness classes for degenerate elliptic problems in \begin{document}$ {\mathbb R}^N $\end{document} under the form id="M2">\begin{document}$ u = \Delta {{\varphi}}(x,u)+f(x) $\end{document}, with locally (in id="M3">\begin{document}$ $\end{document}</inline-fo...

We construct cosmological models based on a complex scalar field with power-law potential $V=\frac{K}{\ensuremath{\gamma}\ensuremath{-}1}(\frac{m}{\ensuremath{\hbar}}{)}^{2\ensuremath{\gamma}}|\ensuremath{\varphi}{|}^{2\ensuremath{\gamma}}$ associated polytropic equation of state $P=K{\ensuremath{\rho}}^{\ensuremath{\gamma}}$ (the an isothermal $P=\ensuremath{\rho}{k}_{B}T/m$ is $V=\frac{m{k}_{...

"In this paper, we investigate the relations between growth of entire coefficients and that solutions complex homogeneous non-homogeneous linear difference equations with $% \varphi $-order by using a slow scale, $\varphi $-order, where $ is non-decreasing unbounded function. We extend some precedent results due to Zheng Tu (2011) [15] others."

We continue the study from [1], by studying equations of type $\psi(n) = \dfrac{k+1}{k} \cdot \ n+a,$ $a\in \{0, 1, 2, 3\},$ and $\varphi(n) \dfrac{k-1}{k} n-a,$ 3\}$ for $k &gt; 1,$ where $\psi(n)$ $\varphi(n)$ denote Dedekind, respectively Euler's, arithmetical functions.

A bstract In this work, we propose a string-inspired two fields inflation model to address the fine-tuning problem that standard suffers. The fast-rolling tachyon $$ \mathcal{T} T originated from D-brane and anti-D-brane pair annihilation locks inflaton φ slowly rolling on Higgs-like potential V\left(\varphi ...

Let \(\theta \) be an irrational number and \(\varphi a real number. \(C > 2\) \(\varepsilon 0\). There are infinitely many positive integers n free of prime factors \(> (\log )^C\), such that \(\Vert \theta + \varphi \Vert < n^{-\left( \frac{1}{3} - \frac{2}{3C}\right) \varepsilon }\). Here y\Vert is the distance from y to \(\mathbb Z\).