Navegando por Autor "Assunção, Ronaldo Brasileiro"

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Existence and multiplicity of solutions for a supercritical elliptic problem in unbounded cylinders.
(2017) Assunção, Ronaldo Brasileiro; Miyagaki, Olimpio Hiroshi; Rodrigues, Bruno Mendes
We consider the following elliptic problem: – div( |∇u| p–2∇u |y| ap ) = |u| q–2u |y| bq + f(x) in , u = 0 on ∂, in an unbounded cylindrical domain := (y,z) ∈ Rm+1 × RN–m–1;0< A < |y| < B < ∞ , where 1 ≤ m < N – p, q = q(a, b) := Np N–p(a+1–b) , p > 1 and A, B ∈ R+. Let p∗ N,m := p(N–m) N–m–p . We show that p∗ N,m is the true critical exponent for this problem. The starting point for a variational approach to this problem is the known Maz’ja’s inequality (Sobolev Spaces, 1980) which guarantees, for the q previously defined, that the energy functional associated with this problem is well defined. This inequality generalizes the inequalities of Sobolev (p = 2, a = 0 and b = 0) and Hardy (p = 2, a = 0 and b = 1). Under certain conditions on the parameters a and b, using the principle of symmetric criticality and variational methods, we prove that the problem has at least one solution in the case f ≡ 0 and at least two solutions in the case f ≡ 0, if p < q < p∗ N,m.
Existence and multiplicity results for an elliptic problem involving cylindrical weights and a homogeneous term μ.
(2019) Assunção, Ronaldo Brasileiro; Miyagaki, Olimpio Hiroshi; Leme, Leandro Correia Paes; Rodrigues, Bruno Mendes
We consider the following elliptic problem ⎧⎨ ⎩ − div |∇u| p−2 ∇u |y| ap = μ |u| p−2 u |y| p(a+1) + h(x) |u| q−2 u |y| bq + f(x, u) in Ω, u = 0 on ∂Ω, in an unbounded cylindrical domain Ω := {(y, z) ∈ Rm+1 × RN−m−1 ; 0 1, 1 ≤ m
On a class of nonhomogeneous equations of Hénon-type : symmetry breaking and non radial solutions.
(2017) Assunção, Ronaldo Brasileiro; Miyagaki, Olimpio Hiroshi; Pereira, Gilberto de Assis; Rodrigues, Bruno Mendes
In this work we study the following Hénon-type equation ⎧⎪⎨ ⎪⎩ −div ( |∇u|p−2∇u |x|ap ) = |x|βf(u), in B; u > 0, in B; u = 0, on ∂B; where B := { x ∈ RN ; |x| < 1 } is a ball centered at the origin, the parameters verify the inequalities 0 ≤ a < N−p p , N ≥ 4, β > 0, 2 ≤ p < Np+pβ N−p(a+1) , and the nonlinearity f is nonhomogeneous. By minimization on the Nehari manifold, we prove that for large values of the parameter β there is a symmetry breaking and non radial solutions appear.