Artigos
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Item Curves with no tritangent planes in space and their convex envelopes(Journal of Geometry, 1990-11) Ballesteros, Juan J. Nuño; Fuster, M. Carmen RomeroItem Semilinear elliptic equations with the primitive of the nonlinearity away from the spectrum(Nonlinear Analysis: Theory, Methods & Applications, 1991) Miyagaki, Olimpio H.; Figueiredo, Djairo G.deItem A four vertex theorem for strictly convex space curves(Journal of Geometry, 1993-03) Ballesteros, Juan J. Nuño; Fuster, M. Carmen RomeroItem Meio de cultura e condição ideais para germinar o pólen de Lycopersicon esculentum Mill. cv. Santa Cruz Kada(Revista Ceres, 1995-05) Oliveira, Laede Maffia de; Almeida, Élcio Cruz de; Lima, José Oscar Gomes de; Lacerda, Cynthia Araújo deNa germinação de pólen in vitro, dois fatores são de primordial importância: um meio de cultura que possibilite o máximo de germinação, e o ambiente propício à sua ocorrência. Com o objetivo de encontrá-los, foi feita esta pesquisa. Observou-se à taxa de germinação de pólen de plantas do cv. Santa Cruz Kada em soluções de sacarose a várias concentrações, em laboratório, sob luz difusa e à temperatura ambiente com leituras de hora em hora por 24 horas; em oito meios de cultura sólidos, por 36 horas e com leituras a intervalos de 12 horas; à temperatura ambiente, sob luz difusa e sob luz fluorescente de 40 W a 40 cm da placa de Petri com o meio; e em estufa incubadora a 22 ± 2ºC e sob luz fluorescente de 40 W a 40 cm da placa com o meio. 0 pólen foi coletado quando fértil e viável. Paralelamente, testaram-se os efeitos dos meios de cultura, dos níveis de sacarose e dos tempos de incubação sobre a germinação do pólen, por meio de análise de variância e ajustamento de equações de regressão dos dados., usando as variáveis quantitativas níveis de sacarose, tempos de incubação e a variável qualitativa meio de cultura. Para esta, utilizou-se a variável "dummy“ em que se ajusta um plano de regressão e dele se extraem equações, substituindo-se a variável qualitativa por variáveis codificadas quantitativamente. O pólen germinou mais (até 96%) no meio com 0,5% de ágar, 50 ppm de [13303 e 10% de sacarose e incubado em estufa, a 22 :!:. ZºC, sob luz fluorescente de 40 W a 404 cm da placa com o meio. Nesta condição, o pólen do mesmo cultivarsofreu influência do meio de cultura isolado e em conjunto com os níveis de sacarose; dos níveis de sacarose isoladamente e associados aos meios e aos tempos de incubação ou só associados aos tempos de incubação, a 1% de probabilidade, na diferença das respostas da percentagem de sua germinação.Item Variational inequality for a nonlinear model of the oscillations of beams(Nonlinear Analysis: Theory, Methods & Applications, 1997-03) Alves, Margareth da SilvaItem Critical singular problems on unbounded domains(Abstract and Applied Analysis, 2004-04-30) Morais Filho, D. C. de; Miyagaki, O. H.We present some results of existence for the following problem: − ∆u = a(x)g(u)+u | u | 2 − 2 , x ∈ R N (N ≥ 3), u ∈ D 1,2 ( R N ), where the function a is a sign-changing function with a singularity at the origin and g has growth up to the Sobolev critical exponent 2 ∗ = 2N/(N − 2).Item A Robin problem for a class of quasilinear operators and a related minimizing problem(Nonlinear Analysis: Theory, Methods & Applications, 2004-10) Miyagaki, Olímpio Hiroshi; Abreu, Emerson A. M. deIn this paper we establish the existence of multiple radial solutions for a class of quasilinear operators with nonlinear boundary Robin conditions. Besides other conditions, we consider the nonlinearities having a behavior at -∞ at least like a linearity of slope less than first eigenvalue λ1(R). The technical approach is by variational methods, which is mainly based on a version of Mountain Pass Theorem due to Ghoussoub and Preiss.Item Multiplicity of solutions for critical singular problems(Applied Mathematics Letters, 2006-08) Miyagaki, Olimpio Hiroshi; Assuncao, Ronaldo B.; Carrião, Paulo CesarIn this work we deal with the class of critical singular quasilinear elliptic problems in R N of the form −div(|x|−ap |∇u| p−2 ∇u) = α|x|−bq |u|q−2 u + β|x|−dr k|u|r−2 u x ∈ RN , (P) where 1 < p < N, a < N/ p, a ≤ b < a + 1, α and β are positive parameters, q = q(a, b) ≡ N p/[N − p(a + 1 − b)] and d ∈ R. q/(q−r) Moreover, 1 < r < p∗ = N p/(N − p) and 0 ≤ k ∈ L r(d−b) (R N ). Multiplicity results are established by combining a version of the concentration–compactness lemma due to Lions with the Krasnoselski genus and the symmetric mountain-pass theorem due to Rabinowitz.Item Stable maps from surfaces to the plane with prescribed branching data(Topology and its Applications, 2007-01-01) Jesus, C. Mendes de; Hacon, D.; Fuster, M.C. RomeroWe consider the problem of constructing stable maps from surfaces to the plane with branch set a given set of curves immersed (except possibly with cusps) in the plane. Various constructions are used (1) piecing together regions immersed in the plane (2) modifying an existing stable map by a sequence of codimension one transitions (swallowtails etc) or by surgeries. In (1) the way the regions are pieced together is described by a bipartite graph (an edge C* corresponds to a branch curve C with the vertices of C* corresponding to the two regions containing C). We show that any bipartite graph may be realized by a stable map and we consider the question of realizing graphs by fold maps (i.e. maps without cusps). For example, using Arnol'd's classification of immersed curves, we list all branch sets with at most two branch curves and four double points realizable by planar fold maps of the torus.Item Critical singular problems via concentration-compactness lemma(Journal of Mathematical Analysis and Applications, 2007-02-01) Miyagaki, Olimpio Hiroshi; Assunção, Ronaldo B.; Carrião, Paulo CesarIn this work we consider existence and multiplicity results of nontrivial solutions for a class of quasilinear degenerate elliptic equations in RN of the form (P)−div[|x|−ap|∇u|p−2∇u]+λ|x|−(a+1)p|u|p−2u=|x|−bq|u|q−2u+f, where x∈RN, 1Item Critical singular problems via concentration-compactness lemma(Journal of Mathematical Analysis and Applications, 2007-02-01) Miyagaki, Olimpio Hiroshi; Assunção, Ronaldo B.; Carrião, Paulo CesarIn this work we consider existence and multiplicity results of nontrivial solutions for a class of quasilinear degenerate elliptic equations in RN of the form (P)−div[|x|−ap|∇u|p−2∇u]+λ|x|−(a+1)p|u|p−2u=|x|−bq|u|q−2u+f, where x∈RN, 1Item Subcritical perturbations of a singular quasilinear elliptic equation involving the critical Hardy–Sobolev exponent(Nonlinear Analysis: Theory, Methods & Applications, 2007-03-15) Miyagaki, O. H.; Assunção, R. B.; Carrião, P. C.In this work we improve some known results for a singular operator and also for a wide class of lower-order terms by proving a multiplicity result. The proof is made by applying the generalized mountain-pass theorem due to Ambrosetti and Rabinowitz. To do this, we show that the minimax levels are in a convenient range by combining a special class of approximating functions, due to Gazzola and Ruf, with the concentrating functions of the best Sobolev constant.Item Stability of closed timelike curves in the Gödel universe(General Relativity and Gravitation, 2007-06-16) Rosa, Valéria M.; Letelier, Patricio S.We study, in some detail, the linear stability of closed timelike curves in the Gödel universe. We show that these curves are stable. We present a simple extension (deformation) of the Gödel metric that contains a class of closed timelike curves similar to the ones associated to the original metric. This extension correspond to the addition of matter whose energy-momentum tensor is analyzed. We find the conditions to have matter that satisfies the usual energy conditions. We study the stability of closed timelike curves in the presence of usual matter as well as in the presence of exotic matter (matter that does satisfy the above mentioned conditions). We find that the closed timelike curves in the Gödel universe with or without the inclusion of regular or exotic matter are stable under linear perturbations. We also find a sort of structural stability.Item On positive solutions for a class of singular quasilinear elliptic systems(Journal of Mathematical Analysis and Applications, 2007-10-15) Miyagaki, O. H.; Rodrigues, R. S.We study through the lower and upper-solution method, the existence of positive weak solution to the quasilinear elliptic system with weights ⎧ ⎪ −div(|x|−ap |∇u|p−2 ∇u) = λ|x|−(a+1)p+c1 uα v γ in Ω, ⎨ −div(|x|−bq |∇v|q−2 ∇v) = λ|x|−(b+1)q+c2 uδ v β in Ω, ⎪ ⎩ u=v=0 on ∂Ω, −p −q where Ω is a bounded smooth domain of RN , with 0 ∈ Ω, 1 < p, q < N , 0 a < N p , 0 b < N q , 0 α < p − 1, 0 β < q − 1, δ, γ , c1 , c2 > 0 and θ := (p − 1 − α)(q − 1 − β) − γ δ > 0, for each λ > 0.Item Stability of closed timelike geodesics(Physics Letters A, 2007-10-15) Rosa, V. M.; Letelier, P. S.The existence and stability under linear perturbations of closed timelike geodesics (CTG) in Bonnor–Ward spacetime is studied in some detail. Regions where the CTG exist and are linearly stable are exhibited.Item Soliton solutions for quasilinear Schrödinger equations: the critical exponential case(Nonlinear Analysis: Theory, Methods & Applications, 2007-12-15) Miyagaki, Olímpio H.; Soares, Sérgio H. M.; Ó, João M. B. doQuasilinear elliptic equations in R2 of second order with critical exponential growth are considered. By using a change of variable, the quasilinear equations are reduced to semilinear equations, whose respective associated functionals are well defined in H 1 (R2) and satisfy the geometric hypotheses of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration–compactness principle [P.L. Lions, The concentration compactness principle in the calculus of variations. The locally compact case. Part I and II, Ann. Inst. H. Poincar ́ Anal. Non. Lineaire 1 (1984) 109–145, 223–283] combined with test functions connected with optimal Trudinger–Moser inequality.Item Non-autonomous perturbations for a class of quasilinear elliptic equations on R(Journal of Mathematical Analysis and Applications, 2008-08-01) Miyagaki, O. H.; Alves, M. J.; Carrião, P. C.This paper is concerned with the existence of two positive solutions for a class of quasilinear elliptic equations on R involving the p-Laplacian, with a non-autonomous perturbation. The first solution is obtained as a local minimum in a neighborhood of 0 and the second one by a mountain-pass argument. The special features of the problem here is the “complex” structure of the linear part which, in particular, oblige to work into the space W 1,p (R). Then one faces problems in the convergence of the sequences of derivatives un → u.Item A comment on Bonnor–Steadman closed timelike curves(General Relativity and Gravitation, 2008-09-07) Rosa, Valéria M.; Letelier, Patricio S.The existence and stability closed timelike curves in a Bonnor–Ward spacetime without torsion line singularities is shown by exhibiting particular examples.Item Geometric contacts of surfaces immersed in R^ n , n ≥ 5(Differential Geometry and its Applications, 2008-12-02) Moraes, S. M.; Costa, S. I. R.; Romero-Fuster, M. C.We study the extrinsic geometry of surfaces immersed in R^ n , n ≥ 5 by analyzing their contacts with different standard geometrical models, such as hyperplanes and hyperspheres. We investigate the relation between different types of contact and the properties of the curvature ellipses at each point. In particular, we focalize our attention on the hyperspheres having contacts of corank two with the surface. This leads in a natural way to the concept of umbilical focus and umbilic curvature.Item Superlinear problems without Ambrosetti and Rabinowitz growth condition(Journal of Differential Equations, 2008-12-15) Miyagaki, O. H.; Souto, M. A. S.Superlinear elliptic boundary value problems without Ambrosetti and Rabinowitz growth condition are considered. Existence of nontrivial solution result is established by combining some arguments used by Struwe and Tarantello and Schechter and Zou (also by Wang and Wei). Firstly, by using the mountain pass theorem due to Ambrosetti and Rabinowitz is constructed a solution for almost every parameter λ by varying the parameter λ. Then, it is considered the continuation of the solutions.
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