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Item How to break the uniqueness of W1,ploc(Ω)Wloc1,p(Ω) -solutions for very singular elliptic problems by non-local terms(Zeitschrift für angewandte Mathematik und Physik, 2018-12) Santos, Carlos Alberto; Santos, LaisIn this paper, we are going to show existence of branches of bifurcation of positive W1,ploc(Ω)Wloc1,p(Ω) -solutions for the very singular non-local λλ -problem −⎛⎝⎜∫Ωg(x,u)dx⎞⎠⎟rΔpu=λ(a(x)u−δ+b(x)uβ) in Ω,u>0 in Ω and u=0 on ∂Ω, −(∫Ωg(x,u)dx)rΔpu=λ(a(x)u−δ+b(x)uβ) in Ω,u>0 in Ω and u=0 on ∂Ω, where Ω⊂RNΩ⊂RN is a smooth bounded domain, δ>0δ>0 , 0<βItem 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 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 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 The ϕ-Dimension: A new homological measure(Algebras and Representation Theory, 2015-04) Fernandes, Sônia Maria; Lanzilotta, Marcelo; Hernández, Octavio MendozaIn Igusa and Todorov (2005) introduced two functions ϕ and ψ, which are natural and important homological measures generalising the notion of the projective dimension. These Igusa-Todorov functions have become a powerful tool to understand better the finitistic dimension conjecture. In this paper, for an artin R-algebra A and the Igusa-Todorov function ϕ, we characterise the ϕ-dimension of A in terms of the bi-functors ExtiA(−,−)ExtAi(−,−) and in terms of Tor’s bi-functors TorAi(−,−).ToriA(−,−). Furthermore, by using the first characterisation of the ϕ-dimension, we show that the finiteness of the ϕ-dimension of an artin algebra is invariant under derived equivalences. As an application of this result, we generalise the classical Bongartz’s result (Bongartz, Lect. Notes Math. 903, 26–38, (1981), Corollary 1) as follows: For an artin algebra A, a tilting A-module T and the endomorphism algebra B = End A (T) o p , we have that ϕ dim (A) − pd T ≤ ϕ dim (B) ≤ ϕ dim (A) + pd T.Item Generalized edge-pairings for the family of hyperbolic tessellations {10λ,2λ}(Computational and Applied Mathematics, 2016-04) Faria, Mercio Botelho; Vieira, Vandenberg Lopes; Palazzo Jr., ReginaldoIn this paper we present generalized edge-pairings for the family of hyperbolic tessellations {10λ,2λ}{10λ,2λ} , with the purpose to obtain the corresponding discrete group of isometries. These tessellations have greater density packing than the self-dual tessellations {4λ,4λ}{4λ,4λ} implying that the associated codes achieve the least error probability, or equivalently, that these codes are optimum codes.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 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 Stabilization of mixture of two rigid solids modeling temperature and porosity(Applied Mathematics Letters, 2012-05) Alves, Margareth S.; Rivera, Jaime E. Muñoz; Sepúlveda, Mauricio; Villagrán, Octavio P. VeraIn this paper we investigate the asymptotic behavior of solutions to the initial boundary value problem for a mixture of two rigid solids modeling temperature and porosity. Our main result is to establish conditions which ensure the analyticity and the exponential stability of the corresponding semigroup.Item Renormalization and forcing of horseshoe orbits(Topology and its Applications, 2014-08-15) Mendoza, ValentínIn this paper we deal with the Boyland forcing of horseshoe orbits. We prove that there exists a set R of renormalizable horseshoe orbits containing only quasi-one-dimensional orbits, that is, for these orbits the Boyland order coincides with the unimodal order.