We consider gravity mediated by non-metricity, with vanishing curvature and torsion. The gravitational action, including an arbitrary function of the non-metric scalar, is investigated in view characterizing dark energy effects. In particular, we present a method to reconstruct $f(Q)$ action without resorting \emph{a priori} assumptions on cosmological model. To this purpose, adopt based ration...

In this work we consider the fractional Kirchhoff equations with singular nonlinearity, $$\displaylines{ M\Big( \int_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^p}{|x-y|^{N+sp}}dx dy\Big) (-\Delta)^s_p u = \lambda a(x)|u|^{q-2}u +\frac{1-\alpha}{2-\alpha-\beta} c(x)|u|^{-\alpha}|v|^{1-\beta}, \quad \text{in }\Omega,\cr \int_{\mathbb{R}^{2N}}\frac{|v(x)-v(y)|^p}{|x-y|^{N+sp}}dx v \mu b(x)|v|^{q-2}v +\fra...

"In this paper, we obtain certain generalizations of some results from [13] and [14]. Let $\Phi_{n, \alpha, \beta}$ be the extension operator introduced in \cite{GrahamHamadaKohrSuffridge} let Q}$ [7]. $a \in \C$, $b \R$ such that $|1-a| < b \leq {\rm Re}\ a$. We consider Janowski classes $S^*(a,b, \B)$ $\A S^*(a,b, with complex coefficients [16]. In case $n=1$, denote \mathbb{B}^1)$ by $S^*...

Motivated by recent attempts to quantum simulate lattice models with continuous Abelian symmetries using discrete approximations, we define an extended-O(2) model adding a $\gamma \cos(q\varphi)$ term the ordinary O(2) angular values restricted $2\pi$ interval. In \rightarrow \infty$ limit, becomes extended $q$-state clock that reduces when $q$ is integer and otherwise continuation of for nonin...

This article deals with the study of following singular quasilinear equation: $$\begin{aligned} (P) \left\{ \ -\Delta _{p}u _{q}u = f(x) u^{-\delta },\; u>0 \text { in }\; \Omega ; \; u=0 on } \partial , \right. \end{aligned}$$ where $$\Omega $$ is a bounded domain $${\mathbb {R}}^N$$ $$C^2$$ boundary $$\partial $$1< q< p<\infty $$\delta >0$$ and $$f\in L^\infty _{loc}(\Omega )$$ non-negative f...

In this paper we strengthen to Morrey-Lorentz spaces the famous trace principle introduced by Adams. More precisely, show that Riesz potential $I_{\alpha}$ is continuous \begin{equation} \Vert I_{\alpha}f\Vert_{\mathcal{M}_{q, \infty}^{\lambda_{\ast}}(d\mu)}\lesssim \Arrowvert\mu\Arrowvert_{\beta}^{{1}/{q}}\,\Vert f\Vert_{\mathcal{M}_{p, \infty}^{\lambda}(d\nu)}\nonumber\\[0.02in] \end{equation...

Here, we study the Fučik spectrum for $ p, q $-Laplacian$ -\Delta_p u-\Delta_q u = \alpha \left((u^+)^{p-1}+(u^+)^{q-1}\right)-\beta \left((u^-)^{p-1}+(u^-)^{q-1}\right) $in a bounded domain \Omega in \mathbb{R}^N ($ N\geq1 $), with Dirichlet boundary condition and 1&lt;q&lt;p&lt;\infty $.