8 papers
Elliptic problems involving a diffusion operator of vectorial -Laplacian type
M. L. M. Carvalho, J. R. Santos, H. W. G. Silva
We study a broad class of anisotropic Dirichlet problems driven by the nonhomogeneous operator \[ \mathcal L_Au=-\sum_{i=1}^N\partial_i\!\left( a_i(|\partial_i u|^{p_i})|\partial_i…
Extremal parameters, multiplicity and nonexistence for a singular elliptic problem
J. C. de Albuquerque, M. L. M. Carvalho, Edcarlos D. Silva +1
We consider the following class of singular elliptic problems \[ \begin{cases} -Δu = -\dfrac{u}{|u|^{β+1}}χ_{\{|u|>0\}} +λ|u|^{p-1}u, & \text{in }Ω,\\[1mm] u=0, & \text{on }\partia…
Superlinear fractional -Laplacian type problems via the nonlinear Rayleigh quotient with two parameters
L. R. S. de Assis, M. L. M. Carvalho, Edcarlos D. Silva +1
In this work, we establish the existence and multiplicity of weak solutions for nonlocal elliptic problems driven by the fractional -Laplacian operator, in the presence of a sig…
Multiplicity of solutions for singular elliptic problems with Stein-Weiss term
Márcia S. B. A. Cardoso, Edcarlos D. Silva, Marcos. L. M. Carvalho +1
In the present work, we establish the existence and multiplicity of positive solutions for the singular elliptic equations with a double weighted nonlocal interaction term defined…
Stein-Weiss problems via nonlinear Rayleigh quotient for concave-convex nonlinearities
Edcarlos D. Silva, Marcos. L. M. Carvalho, Márcia S. B. A. Cardoso
In the present work, we consider existence and multiplicity of positive solutions for nonlocal elliptic problems driven by the Stein-Weiss problem with concave-convex nonlinearitie…
Quasilinear elliptic problems via nonlinear Rayleigh quotient
Edcarlos D. Silva, Marcos L. M. Carvalho, Leszek Gasinski +1
It is established existence and multiplicity of solution for the following class of quasilinear elliptic problems $$ \left\{ \begin{array}{lr} -Δ_Φu = λa(x) |u|^{q-2}u + |u|^{p-2}u…
Asymptotic behavior of Musielak-Orlicz-Sobolev modulars
J. C. de Albuquerque, L. R. S. de Assis, M. L. M. Carvalho +1
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 Bou…
On Fractional Musielak-Sobolev spaces and applications to nonlocal problems
J. C. de Albuquerque, L. R. S. de Assis, M. L. M. Carvalho +1
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…