Positive solutions of a nonlocal singular elliptic equation by means of a non-standard bifurcation theory

2019 ◽  
Vol 469 (2) ◽  
pp. 897-915
Author(s):  
M. Delgado ◽  
I.B.M. Duarte ◽  
A. Suárez
Keyword(s):  
Elliptic Equation ◽  
Positive Solutions ◽  
Bifurcation Theory ◽  
Singular Elliptic Equation

scholarly journals The existence of positive solutions for Kirchhoff-type problems via the sub-supersolution method

2018 ◽  
Vol 26 (1) ◽  
pp. 5-41 ◽  
Author(s):  
Baoqiang Yan ◽  
Donal O’Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Positive Solutions ◽  
Bifurcation Theory ◽  
Sufficient Conditions ◽  
Global Bifurcation ◽  
Existence Of A Solution ◽  
Kirchhoff Type ◽  
Existence Of Positive Solutions ◽  
Global Bifurcation Theory ◽  
Necessary And Sufficient ◽  
Kirchhoff Type Problems

Abstract In this paper we discuss the existence of a solution between wellordered subsolution and supersolution of the Kirchhoff equation. Using the sub-supersolution method together with a Rabinowitz-type global bifurcation theory, we establish the existence of positive solutions for Kirchhoff-type problems when the nonlinearity is singular or sign-changing. Moreover, we obtain some necessary and sufficient conditions for the existence of positive solutions for the problem when N = 1.

Positive Solutions for the Generalized Nonlinear Logistic Equations

2016 ◽  
Vol 59 (01) ◽  
pp. 73-86 ◽  
Author(s):  
Leszek Gasiński ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Differential Operator ◽  
Elliptic Equation ◽  
Positive Solutions ◽  
Type Result ◽  
Logistic Equations ◽  
Nonhomogeneous Differential Operator

AbstractWe consider a nonlinear parametric elliptic equation driven by a nonhomogeneous differential operator with a logistic reaction of the superdiòusive type. Using variationalmethods coupled with suitable truncation and comparison techniques, we prove a bifurcation type result describing the set of positive solutions as the parameter varies.

scholarly journals Bifurcation results of positive solutions for an elliptic equation with nonlocal terms

2021 ◽  
Vol 6 (9) ◽  
pp. 9547-9567
Author(s):  
Jiaqing Hu ◽  
◽  
Xian Xu ◽  
Qiangqiang Yang ◽  
Keyword(s):  
Elliptic Equation ◽  
Positive Solutions ◽  
Nonlocal Terms

Free boundary solutions to a log-singular elliptic equation

2013 ◽  
Vol 82 (1-2) ◽  
pp. 91-107 ◽  
Author(s):  
Marcelo Montenegro ◽  
Sebastián Lorca
Keyword(s):  
Elliptic Equation ◽  
Free Boundary ◽  
Singular Elliptic Equation ◽  
Boundary Solutions
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