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https://locus.ufv.br//handle/123456789/23794
Tipo: | Artigo |
Título: | 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. |
Palavras-chave: | Very singular term Uniqueness Non-local Comparison principle |
Editor: | Zeitschrift für angewandte Mathematik und Physik |
Tipo de Acesso: | Springer Nature Switzerland AG |
URI: | https://doi.org/10.1007/s00033-018-1040-8 http://www.locus.ufv.br/handle/123456789/23794 |
Data do documento: | Dez-2018 |
Aparece nas coleções: | Artigos |
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artigo.pdf Until 2100-12-31 | Texto completo | 885,72 kB | Adobe PDF | Visualizar/Abrir ACESSO RESTRITO |
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