Navegando por Autor "Leme, Leandro Correia Paes"
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Item Construções geométricas e padrões islâmicos.(2018) Fialho, Rodnei Eduardo; Carneiro, Luiz Gustavo de Oliveira; Carneiro, Luiz Gustavo de Oliveira; Leme, Leandro Correia Paes; Chaves, Marcio Fialho; Xavier, Sebastião MartinsEste trabalho é o início da produção de um material didático com foco em construções geométricas de padrões islâmicos utilizando régua não graduada e compasso. Nesse material didático tratou-se -se da parte histórica dos padrões geométricos islâmicos; de construções geométricas elementares como bissetrizes, mediatrizes retas perpendiculares e paralelas e de polígonos do triângulo ao decágono e por fim de construções de padrões islâmicos todos utilizando somente régua não graduada e compasso. Todos as construções apresentadas nesse trabalho foram feitas com o auxílio do programa Geogebra.Item 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 MendesWe 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 ≤ mItem Existence of a positive solution for a class of non-local elliptic problem with critical growth in Rn.(2022) Leme, Leandro Correia Paes; Rodrigues, Bruno MendesIn this article, we consider the following non-local elliptic equation with critical growth ⎧⎪⎨⎪⎩− a + b RN |∇u| 2 dx p−1 2 Δu = λk(x)uq + u2∗−1, x ∈ RN , u ∈ D1,2(RN ), where N ≥ 3, λ > 0, 2∗:= 2N N−2 , 1 < p ≤ q < 2∗ − 1, a ≥ 0, b ≥ 0 and k(x) ∈ L 2∗ 2∗−q−1 (RN ) is a nonnegative function. Using variational methods and concentration-compactness principle, we obtain a positive solution.Item Multiplicity of positive solutions for the Kirchhoff-type equations with critical exponent in RN.(2018) Miyagaki, Olimpio Hiroshi; Leme, Leandro Correia Paes; Rodrigues, Bruno MendesIn this work we study the existence and multiplicity of solutions to the following Kirchhofftype problem with critical nonlinearity in RN ⎧⎨ ⎩ − ( a + b ∫ RN |∇u|pdx ) Δpu = μup∗−1 + λf (x, u); x ∈ RN , u ∈ D1,p(RN ), where N ≥ 2p, μ, λ, a, b > 0 and the nonlinearity f (x, u) satisfies certain subcritical growth conditions. By using topological and variational methods, infinitely many positive solutions are obtained.Item Multiplicity of solutions for p-biharmonic problems with critical growth.(2018) Bueno, Hamilton Prado; Leme, Leandro Correia Paes; Rodrigues, Helder CândidoWe prove the existence of infinitely many solutions for p-biharmonic problems in a bounded, smooth domain Ω with concave-convex nonlinearities dependent upon a parameter λ and a positive continuous function f:Ω¯¯¯¯→R. We simultaneously handle critical case problems with both Navier and Dirichlet boundary conditions by applying the Ljusternik-Schnirelmann method. The multiplicity of solutions is obtained when λ is small enough. In the case of Navier boundary conditions, all solutions are positive, and a regularity result is proved.Item On p-biharmonic equations with critical growth.(2021) Leme, Leandro Correia Paes; Rodrigues, Helder Cândido; Bueno, Hamilton PradoWe study p-biharmonic problems dealing with concave-convex nonlinearitiesin the critical case with both Navier and Dirichlet boundary conditions in a bounded, smooth domain and some f ε C(Ω), which is either a positive or a change-sign function. By applying Nehari’s minimization method, we prove the existence of two nontrivial solutions for the problems. If f is positive, both solutions of the problem with Navier boundary condition are positive.