Centro de Ciências Exatas e Tecnológicas
URI permanente desta comunidadehttps://locus.ufv.br/handle/123456789/9791
Navegar
6 resultados
Resultados da Pesquisa
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 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.Item 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 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 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.