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URI permanente para esta coleçãohttps://locus.ufv.br/handle/123456789/11799

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2004 - 200921

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Data inicial: 2000Data final: 2009

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Agora exibindo 1 - 10 de 21
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    Critical singular problems via concentration-compactness lemma
    (Journal of Mathematical Analysis and Applications, 2007-02-01) Miyagaki, Olimpio Hiroshi; Assunção, Ronaldo B.; Carrião, Paulo Cesar
    In 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, 1
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    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. de
    In 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.
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    Critical singular problems via concentration-compactness lemma
    (Journal of Mathematical Analysis and Applications, 2007-02-01) Miyagaki, Olimpio Hiroshi; Assunção, Ronaldo B.; Carrião, Paulo Cesar
    In 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, 1
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    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.
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    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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    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.
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    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. Romero
    We 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.
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    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.
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    Multiplicity of solutions for critical singular problems
    (Applied Mathematics Letters, 2006-08) Miyagaki, Olimpio Hiroshi; Assuncao, Ronaldo B.; Carrião, Paulo Cesar
    In 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.
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    Multiple positive solutions for semilinear Dirichlet problems with sign-changing weight function in infinite strip domains
    (Nonlinear Analysis: Theory, Methods & Applications, 2009-10-01) Miyagaki, O. H.; Miotto, M. L.
    In this paper, existence and multiplicity results to the following Dirichlet problem −∆u + u = λf (x)|u|q−1 + h(x)|u|p−1 , u > 0, u = 0, in Ω in Ω on ∂ Ω are established, where Ω = Ω × R, Ω ⊂ RN −1 is bounded smooth domain and N ≥ 2. Here 1 < q < 2 < p < 2∗ 2∗ = N2N2 if N ≥ 3, 2∗ = ∞ if N = 2 , λ is a positive real − parameter, the function f , among other conditions, can possibly change sign in Ω , and the function h satisfies suitable conditions. The study is based on the comparison of energy levels on Nehari manifold.