DSpace Coleção: Artigos Técnico-científicos na área de MatemáticaArtigos Técnico-científicos na área de Matemáticahttps://locus.ufv.br//handle/123456789/117992021-11-29T03:52:18Z2021-11-29T03:52:18ZHow to break the uniqueness of W1,ploc(Ω)Wloc1,p(Ω) -solutions for very singular elliptic problems by non-local termsSantos, Carlos AlbertoSantos, Laishttps://locus.ufv.br//handle/123456789/237942019-03-07T12:32:14Z2018-12-01T00:00:00ZTítulo: How to break the uniqueness of W1,ploc(Ω)Wloc1,p(Ω) -solutions for very singular elliptic problems by non-local terms
Autor(es): Santos, Carlos Alberto; Santos, Lais
Abstract: In 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<β<p−10<β<p−1 , a and b are nonnegative measurable functions and g is a positive continuous function. Our approach is based on sub- supersolutions techniques, fixed point theory, in the study of W1,ploc(Ω)Wloc1,p(Ω) -topology of a solution application and a new comparison principle for sub-supersolutions in W1,ploc(Ω)Wloc1,p(Ω) to a problem with p-Laplacian operator perturbed by a very singular term at zero and sublinear at infinity.
Tipo: Artigo2018-12-01T00:00:00ZSemilinear elliptic equations with the primitive of the nonlinearity away from the spectrumMiyagaki, Olimpio H.Figueiredo, Djairo G.dehttps://locus.ufv.br//handle/123456789/236322019-02-21T12:38:16Z1991-01-01T00:00:00ZTítulo: Semilinear elliptic equations with the primitive of the nonlinearity away from the spectrum
Autor(es): Miyagaki, Olimpio H.; Figueiredo, Djairo G.de
Tipo: Artigo1991-01-01T00:00:00ZCritical singular problems via concentration-compactness lemmaMiyagaki, Olimpio HiroshiAssunção, Ronaldo B.Carrião, Paulo Cesarhttps://locus.ufv.br//handle/123456789/236252019-02-20T18:11:32Z2007-02-01T00:00:00ZTítulo: Critical singular problems via concentration-compactness lemma
Autor(es): Miyagaki, Olimpio Hiroshi; Assunção, Ronaldo B.; Carrião, Paulo Cesar
Abstract: 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<p<N, q=q(a,b)≡Np/[N−p(a+1−b)], λ is a parameter, 0⩽a<(N−p)/p, a⩽b⩽a+1, and f∈(Lbq(RN))∗. We look for solutions of problem (P) in the Sobolev space Da1,p(RN) and we prove a version of a concentration-compactness lemma due to Lions. Combining this result with the Ekeland's variational principle and the mountain-pass theorem, we obtain existence and multiplicity results.
Tipo: Artigo2007-02-01T00:00:00ZA Robin problem for a class of quasilinear operators and a related minimizing problemMiyagaki, Olímpio HiroshiAbreu, Emerson A. M. dehttps://locus.ufv.br//handle/123456789/236242019-02-20T18:07:20Z2004-10-01T00:00:00ZTítulo: A Robin problem for a class of quasilinear operators and a related minimizing problem
Autor(es): Miyagaki, Olímpio Hiroshi; Abreu, Emerson A. M. de
Abstract: 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.
Tipo: Artigo2004-10-01T00:00:00Z