Continuums of positive solutions for classes of non-autonomous and non-local problems with strong singular term

被引：3

作者：

Santos, Carlos Alberto ^{[1
]}

Santos, Lais ^{[2
]}

Mishra, Pawan Kumar ^{[3
]}

机构：

[1] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil

[2] Univ Vicosa, Dept Matemat, BR-36570000 Vicosa, MG, Brazil

[3] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba, Brazil

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2019年 / 131卷

关键词：

Strongly-singular nonlinearities; Non-local Kirchhoff problems; Comparison principle for W-loc(1; p)(Omega) sub and supersolutions; Bifurcation theory; KIRCHHOFF-TYPE PROBLEMS; EXISTENCE; MULTIPLICITY; LAPLACIAN; EQUATIONS;

D O I：

10.1016/j.matpur.2019.09.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we show existence of continuums (closed and connected sets in R x C-0 ((Omega) over bar)) of positive solutions for non-local quasilinear problems with strongly-singular reaction term on a bounded domain in R-N with N >= 2. We approached non-autonomous and non-local equations by applying the Bifurcation Theory to the corresponding epsilon-perturbed problems and using a comparison principle for W-loc(1,p)(Omega)-sub and supersolutions to obtain qualitative properties of the epsilon-continuum limit. Moreover, this technique empowers us to study a strongly-singular and non-homogeneous Kirchhoff problem to get the existence of a continuum of positive solutions. (C) 2019 Elsevier Masson SAS. All rights reserved.

引用

页码：225 / 250

页数：26

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