Searcharxiv⌕ Search

arXiv subjects

Anderson L. A. de Araujo

Publications and source records attributed to Anderson L. A. de Araujo.

14 recordsLinked to original sources
arXiv2026

Cohomogeneity one Einstein metrics on complex projective spaces

We study Einstein metrics on complex projective spaces that are invariant under cohomogeneity one actions of compact connected Lie groups, under the assumption that the singular orbits are totally geodesic. These actions were classified by Takagi into five models. For each of them, we write the Einstein equation for diagonal invariant metrics and determine the corresponding smoothness conditions at the singular orbits. Our main result is the nonexistence of smooth globally defined diagonal invariant Einstein metrics with totally geodesic singular orbits in four of the five models and a necessary condition for global existence in the remaining one.

math.DG↗
arXiv2024

Positive solutions of singular elliptic problems with unbounded exponents and unbounded convection term

In this paper, we study the existence of a solution for a class of Dirichlet problems with a singularity and a convection term. Precisely, we consider the existence of a positive solution to the Dirichlet problem $$-Δ_p u = \fracλ{u^α} + f(x,u,\nabla u)$$ in a bounded, smooth domain $Ω$. The convection term has exponents with no upper limitations neither in $u$ nor in $\nabla u$. This is somewhat unexpected and rare. So, we address a wide range of problems not yet contained in the literature. The solution of the problem combines the definition of an auxiliary problem, the method of sub- and super-solution and Schauder's fixed point theorem.

math.AP↗
arXiv2023

The limiting behavior of solutions to p-Laplacian problems with convection and exponential terms

We consider, for $a,l\geq1,$ $b,s,α>0,$ and $p>q\geq1,$ the homogeneous Dirichlet problem for the equation $-Δ_{p}u=λu^{q-1}+βu^{a-1}\left\vert \nabla u\right\vert ^{b}+mu^{l-1}e^{αu^{s}}$ in a smooth bounded domain $Ω\subset\mathbb{R}^{N}.$ We prove that under certain setting of the parameters $λ,$ $β$ and $m$ the problem admits at least one positive solution. Using this result we prove that if $λ,β>0$ are arbitrarily fixed and $m$ is sufficiently small, then the problem has a positive solution $u_{p},$ for all $p$ sufficiently large. In addition, we show that $u_{p}$ converges uniformly to the distance function to the boundary of $Ω,$ as $p\rightarrow\infty.$ This convergence result is new for nonlinearities involving a convection term.

math.AP↗
arXiv2020

Existence, nonexistence, and asymptotic behavior of solutions for $N$-Laplacian equations involving critical exponential growth in the whole $\mathbb{R}^N$

In this paper, we are interested in studying the existence or non-existence of solutions for a class of elliptic problems involving the $N$-Laplacian operator in the whole space. The nonlinearity considered involves critical Trudinger-Moser growth. Our approach is non-variational, and in this way, we can address a wide range of problems not yet contained in the literature. Even $W^{1,N}(\mathbb{R}^N)\hookrightarrow L^\infty(\mathbb{R}^N)$ failing, we establish $\|u_λ\|_{L^\infty(\mathbb{R}^N)} \leq C \|u\|_{W^{1,N}(\mathbb{R}^N)}^Θ$ (for some $Θ>0$), when $u$ is a solution. To conclude, we explore some asymptotic properties.

math.AP↗
arXiv2019

Positive solutions for non-variational fractional elliptic systems with negative exponents

In this paper, we study strongly coupled elliptic systems in non-variational form with negative exponents involving fractional Laplace operators. We investigate the existence, nonexistence, and uniqueness of the positive classical solution. The results obtained here are a natural extension of the results obtained by Ghergu (2010), for the fractional case.

math.AP↗
arXiv2019

An analysis of a mathematical model describing the growth of a tumor treated with chemotherapy

We present a mathematical analysis of a mixed ODE-PDE model describing the spatial distribution and temporal evolution of tumor and normal cells within a tissue subject to the effects of a chemotherapeutic drug. The model assumes that the influx of chemotherapy is restricted to a limited region of the tissue, mimicking a blood vessel passing transversely. We provide results on the existence and uniqueness of the model solution and numerical simulations illustrating different model behaviors.

math.AP↗
arXiv2019

An Analysis of a Mathematical Model Describing Acid-mediated Tumor Invasion

We present a mathematical analysis of a reaction-diffusion model describing acid-mediated tumor invasion. The model describes the spatial distribution and temporal evolution of tumor cells, normal cells, and excess lactic acid concentration. The model assumes that tumor-induced alteration of microenvironmental pH provides a simple but complete mechanism for cancer invasion. We provide results on the existence and uniqueness of a solution considering Neumann and Dirichlet boundary conditions. We also provide numerical simulations to the solutions considering both boundary conditions.

math.AP↗
arXiv2018

Solvability of the asymmetric Bingham fluid equations

In this work, we investigate the asymmetric Bingham fluid equations. The asymmetric fluid of Bingham includes symmetric and antisymmetric stresses with such stresses appearing as an elastic response to the micro-rotational deformations of grains in a complex fluid. We show the global-in-time solvability of a weak solution for three dimensional boundary value problem with Navier boundary conditions of the asymmetric Bingham fluid equations.

math.AP↗
arXiv2017

Some results on Ricatti Equations, Floquet Theory and Applications

In this paper, we present two new results to the classical Floquet theory, which provides the Floquet multipliers for two classes of the planar periodic system. One these results provides the Floquet multipliers independently of the solution of system. To demonstrate the application of these analytical results, we consider a cholera epidemic model with phage dynamics and seasonality incorporated.

math.CA↗
arXiv2017

On Moment Condition and Center Condition for Abel Equation

In this paper we consider Abel equation $x' = g(t)x^2+f(t)x^3$, where $f$ and $g$ are analytical functions. We proved that if the equation has a center at $x=0$, then the Moment Conditions, i. e., $m_k=\int_{-1}^1f(t)(G(t))^kdt=0,~~k=0,1,2$, is satisfied where $G(t)=\int_{-1}^tg(s)ds$. Besides, we give partial a positive answer to a conjecture proposed by Y. Lijun and T. Yun in 2001.

math.CA↗
arXiv2017

Conditions to the existence of center in planar systems and center for Abel equations

Abel equations of the form $x'(t)=f(t)x^3(t)+g(t)x^2(t)$, $t \in [-a,a]$, where $a>0$ is a constant, $f$ and $g$ are continuous functions, are of interest because of their close relation to planar vector fields. If $f$ and $g$ are odd functions, we prove, in this paper, that the Abel equation has a center at the origin. We also consider a class of polynomial differential equations $\dot{x} = -y+P_n(x,y)$ and $\dot{y} = x+Q_n(x,y)$, where $P_n$ and $Q_n$ are homogeneous polynomials of degree $n$. Using the results obtained for Abel's equation, we obtain a new subclass of systems having a center at the origin.

math.CA↗