arXiv subjects

J. C. de Albuquerque

Publications and source records attributed to J. C. de Albuquerque.

5 recordsLinked to original sources

arXiv2025

A class of Hartree-Fock systems with null mass via Nehari-Pohozaev with logarithmic interactions

We establish the existence and qualitative properties of nontrivial solutions for a class of Hartree-Fock type systems defined over the whole space $\mathbb{R}^2$. By introducing a suitable Nehari-Pohozaev manifold, we prove the existence, regularity and we describe the asymptotic behavior of solutions with respect to the interaction parameter $β> 0$. In particular, we show that the system admits either a vector ground state or a semitrivial ground state solution, depending on the magnitude of $β$.

math.AP↗

arXiv2023

Asymptotic behavior of Musielak-Orlicz-Sobolev modulars

In this article we study the asymptotic behavior of anisotropic nonlocal nonstandard growth seminorms and modulars as the fractional parameter goes to 1. This gives a so-called Bourgain-Brezis-Mironescu type formula for a very general family of functionals. In the particu\-lar case of fractional Sobolev spaces with variable exponent, we point out that our proof asks for a weaker regularity of the exponent than the considered in previous articles.

math.AP↗

arXiv2023

On Fractional Musielak-Sobolev spaces and applications to nonlocal problems

In this work, we establish some abstract results on the perspective of the fractional Musielak-Sobolev spaces, such as: uniform convexity, Radon-Riesz property with respect to the modular function, $(S_{+})$-property, Brezis-Lieb type Lemma to the modular function and monotonicity results. Moreover, we apply the theory developed to study the existence of solutions to the following class of nonlocal problems \begin{equation*} \left\{ \begin{array}{ll} (-Δ)_{Φ_{x,y}}^s u = f(x,u),& \mbox{in }Ω, u=0,& \mbox{on }\mathbb{R}^N\setminus Ω, \end{array} \right. \end{equation*} where $N\geq 2$, $Ω\subset \mathbb{R}^N$ is a bounded domain with Lipschitz boundary $\partial Ω$ and $f:Ω\times \mathbb{R} \rightarrow \mathbb{R}$ is a Carathéodory function not necessarily satisfying the Ambrosetti-Rabinowitz condition. Such class of problems enables the presence of many particular operators, for instance, the fractional operator with variable exponent, double-phase and double-phase with variable exponent operators, anisotropic fractional $p$-Laplacian, among others.

math.AP↗

arXiv2021

Regularity results for quasilinear elliptic problems driven by the fractional $Φ$-Laplacian operator

It is established $L^{p}$ estimates for the fractional $Φ$-Laplacian operator defined in bounded domains where the nonlinearity is subcritical or critical in a suitable sense. Furthermore, using some fine estimates together with the Moser's iteration, we prove that any weak solution for fractional $Φ$-Laplacian operator defined in bounded domains belongs to $L^\infty(Ω)$ under appropriate hypotheses on the $N$-function $Φ$. Using the Orlicz space and taking into account the fractional setting for our problem the main results are stated for a huge class of nonlinear operators and nonlinearities.

math.AP↗

arXiv2018

Revised regularity results for quasilinear elliptic problems driven by the $Φ$-Laplacian operator

It is establish regularity results for weak solutions of quasilinear elliptic problems driven by the well known $Φ$-Laplacian operator given by \begin{equation*} \left\{\ \begin{array}{cl} \displaystyle-Δ_Φu= g(x,u), & \mbox{in}~Ω, u=0, & \mbox{on}~\partial Ω, \end{array} \right. \end{equation*} where $Δ_Φu :=\mbox{div}(ϕ(|\nabla u|)\nabla u)$ and $Ω\subset\mathbb{R}^{N}, N \geq 2,$ is a bounded domain with smooth boundary $\partialΩ$. Our work concerns on nonlinearities $g$ which can be homogeneous or non-homogeneous. For the homogeneous case we consider an existence result together with a regularity result proving that any weak solution remains bounded. Furthermore, for the non-homogeneous case, the nonlinear term $g$ can be subcritical or critical proving also that any weak solution is bounded. The proofs are based on Moser's iteration in Orclicz and Orlicz-Sobolev spaces.

math.AP↗