Rodrigo da Silva Rodrigues

TL;DR: In this paper, the existence of positive weak solutions to the quasilinear elliptic system was studied through the lower and upper-solution method, and it was shown that there exists a positive weak solution to the system with weights { − div ( | x | − b q | ∇ v | p − 2 ∇ u | p + c 1 u α v γ + c 2 u δ v β in Ω, u = v = 0 on ∂ Ω, where Ω is a bounded smooth domain of R N, with

TL;DR: In this article, the existence and multiplicity of weak solutions for a general class of quasilinear problems with Dirichlet boundary conditions with variable exponents without Ambrosetti and Rabinowitz (A-R) type growth conditions were established.

TL;DR: In this paper, the authors show that the problem has at least one solution, which converges to zero, in the norm of the space X as a function of the variable exponent spaces with critical growth.

TL;DR: In this paper, the existence and nonexistence of nonnegative weak solutions for a class of degenerate quasilinear elliptic problems with weights and nonlinearity involving the critical Hardy-Sobolev exponent and a sign-changing function were investigated.

TL;DR: In this paper, the existence of sign-changing solutions for a non-local problem involving the fractional Laplacian operator and critical growth nonlinearities was studied, namely (−Δ)su=λf(x,u)