10 citations · 54 across the 45 of their papers we have counts for
50 papers
A nonlocal elliptic problem on a Heisenberg group
Debajyoti Choudhuri, Lamine Mbarki, Olimpio Hiroshi Miyagaki
We study an elliptic nonlocal problem driven by a source term which is a Radon measure. We prove the existence of a weak solution by a weak convergence method. In the process, we d…
Existence of solutions for elliptic problems involving the -Laplacian operator and a discontinuous superlinear nonlinearity
Marcos A. V. Costa, Olímpio H. Miyagaki, Marcos T. O. Pimenta
In this paper, we study a class of quasilinear elliptic problems involving the Laplacian operator and a discontinuous superlinear nonlinearity governed by the Heaviside fun…
On compact embeddings in and fractional spaces
Hamilton Bueno, Aldo Medeiro, Olimpio Miyagaki +1
The study of the fractional Laplacian operator in with Dirichlet boundary conditions gained enormous momentum through its identification with a Neumann oper…
Global bifurcations of nodal solutions for coupled elliptic equations
Haoyu Li, Olímpio Hiroshi Miyagaki, Zhi-Qiang Wang
We investigate the global bifurcation structure of the radial nodal solutions to the coupled elliptic equations \begin{equation} \left\{ \begin{array}{lr} -Δu+u=u^3+βuv^2\mbox{ in…
Multiple nodal solutions of planar Stein-Weiss equations
Eudes M. Barboza, Eduardo De S. Böer, Olímpio H. Miyagaki +1
In this paper, our goal is to investigate the existence of multiple nodal solutions to a class of planar Stein-Weiss problems involving a nonlinearity with subcritical or criti…
Fractional Sobolev-Choquard critical systems with Hardy term and weighted singularities
Ronaldo B. Assunção, Olímpio H. Miyagaki, Rafaella F. S. Siqueira
In this paper, we consider a fractional p-Laplacian system of equations in the entire space RN with doubly critical singular nonlinearities involving a local critical Sobolev term…
Nonexistence results for a degenerate Goursat type Problem
Carlos Alberto Reyes Peña, Olimpio Hiroshi Miyagaki, Rodrigo da Silva Rodrigues
For a generalization of the Gellerstedt operator with Dirichlet boundary conditions in a Tricomi domain. We establish Pohožaev-type identities and prove the nonexistence of nontriv…
Fractional p-Kirchhoff equation with Sobolev and Choquard singular nonlinearities
Ronaldo Brasileiro Assunção, Olímpio Hiroshi Miyagaki, Rafaella Ferreira dos Santos Siqueira
In the present work, we consider a fractional p-Kirchhoff equation in the entire space R^N featuring doubly nonlinearities, involving a generalized nonlocal Choquard subcritical te…
Normalized solutions to polyharmonic equations with Hardy-type potentials and exponential critical nonlinearities
Bartosz Bieganowski, Olímpio Hiroshi Miyagaki, Jacopo Schino
Via a constrained minimization, we find a solution to the problem \begin{equation*} \begin{cases} (-Δ)^m u+\fracμ{|x|^{2m}}u + λu = ηu^3 + g(u)\\ \int_{\mathbb{R}^{2m}} u^2…
Peridynamics and Anisotropic Fractional Sobolev Spaces with Variable Exponents
Sabri Bahrouni, Julian Fernandez Bonder, Ignacio Ceresa Dussel +1
In this paper, our primary objective is to develop the peridynamic fractional Sobolev space and establish novel BBM-type results associated with it. We also address the peridynamic…
On a fractional harmonic oscillator: existence and inexistence of solution, regularity and decay properties
Hamilton P. Bueno, Aldo H. S. Medeiros, Olimpio H. Miyagaki +1
Under simple hypotheses on the nonlinearity , we consider the fractional harmonic operator problem \begin{equation}\label{abstr}\sqrt{-Δ+|x|^2}\,u=f(x,u)\ \ \textrm{in }\ \mathb…
Normalized solutions for INLS equation with critical Hardy-Sobolev type nonlinearities
Mykael Cardoso, José Francisco de Oliveira, Olímpio Miyagaki
We are interested in finding prescribed -norm solutions to inhomogeneous nonlinear Schrödinger (INLS) equations. For we treat the equation with combined Hardy-Sobolev…
A Liouville-type theorem for the coupled Schrödinger systems and the uniqueness of the sign-changing radial solutions
Haoyu Li, Olímpio Hiroshi Miyagaki
In this paper, we study the sign-changing radial solutions of the following coupled Schrödinger system \begin{equation} \left\{ \begin{array}{lr} -Δu_j+λ_j u_j=μ_j u_j^3+\sum_{i\ne…
The concentration-compactness principle for fractional Orlicz-Sobolev spaces
Sabri Bahrouni, Olimpio Miyagaki
In this paper, we delve into the well-known concentration-compactness principle in fractional Orlicz-Sobolev spaces, and we apply it to establish the existence of a weak solution f…
Fractional Sobolev-Chocard critical equation with Hardy term and weighted singularities
Ronaldo B. Assunção, Olímpio H. Miyagaki, Rafaella F. S. Siqueira
In this paper we consider a fractional -Laplacian equation in the entire space with doubly critical singular nonlinearities involving a local critical Sobolev t…
A critical neumann problem with anisotropic p-laplacian
Gustavo F. Madeira, Olímpio H. Miyakaki, Alânnio B. Nóbrega
We are concerned with the existence of solution of the problem $ -Δ^H_pu+|u|^{p-2}u=λ|u|^{q-2}u+ |u|^{p^*-2}u\quad \mbox{in}\quadΩ,$ $u>0\quad \mbox{in}\quadΩ,$ $a(\nabla u)\cdot ν…
Existence and multiplicity results for a class of Kirchhoff-Choquard equations with a generalized sign-changing potential
Eduardo de Souza Böer, Olímpio Hiroshi Miyagaki, Patrizia Pucci
In the present work we are concerned with the following Kirchhoff-Choquard-type equation $$-M(||\nabla u||_{2}^{2})Δu +Q(x)u + μ(V(|\cdot|)\ast u^2)u = f(u) \mbox{ in } \mathbb{R}^…
Existence of normalized solutions for the planar Schrödinger-Poisson system with exponential critical nonlinearity
Claudianor O. Alves, Eduardo de S. Boër, Olímpio H. Miyagaki
In the present work we are concerned with the existence of normalized solutions to the following Schrödinger-Poisson System $$ \left\{ \begin{array}{ll} -Δu + λu + μ(\ln|\cdot|\ast…
Choquard logarithmic equation involving a nonlinearity with exponential critical growth: existence and multiplicity
Eduardo de Souza Böer, Olímpio Hiroshi Miyagaki
The present work is concerned with the following version of Choquard Logarithmic equations $ -Δ_p u -Δ_N u + a|u|^{p-2}u + b|u|^{N-2}u + λ(\ln|\cdot|\ast G(u))g(u) = f(u) \textrm{…
Multiplicity of normalized solutions for a Schrödinger equation with critical growth in
Claudianor O. Alves, Chao Ji, Olimpio H. Miyagaki
In this paper we study the multiplicity of normalized solutions to the following nonlinear Schrödinger equation with critical growth \begin{align*} \left\{ \begin{aligned} &-Δu=λu+…
On the existence and multiplicity of solutions for the -Choquard logarithmic equation with exponential critical growth
Eduardo de Souza Böer, Olímpio Hiroshi Miyagaki
In the present work we briefly explain how to adapt techniques already used in fractional and -fractional Laplacian cases to obtain the existence of a nontrivial solution at the…
Multiplicity of solutions for a scalar field equation involving a fractional -Laplacian with general nonlinearity
Hamilton Bueno, Olimpio Miyagaki, Ailton Vieira
We investigate the existence of infinitely many radially symmetric solutions to the following problem $$(-Δ_p)^s u=g(u) \ \ \textrm{ in } \ \ \mathbb{R}^N, \ \ u\in W^{s,p}(\mathbb…
Normalized solutions for a Schrödinger equation with critical growth in
Claudianor O. Alves, Chao Ji, Olimpio H. Miyagaki
In this paper we study the existence of normalized solutions to the following nonlinear Schrödinger equation with critical growth \begin{align*} \left\{ \begin{aligned} &-Δu=λu+f(u…
The Choquard logarithmic equation involving fractional Laplacian operator and a nonlinearity with exponential critical growth
Eduardo de Souza Böer, Olímpio H. Miyagaki
In the present work we investigate the existence and multiplicity of nontrivial solutions for the Choquard Logarithmic equation $(-Δ)^{\frac{1}{2}} u + au + λ(\ln|\cdot|\ast |u|^{2…