Radial solutions for Neumann problems involving mean curvature operators in Euclidean and Minkowski spaces

2010 ◽  
Vol 283 (3) ◽  
pp. 379-391 ◽  
Author(s):  
Cristian Bereanu ◽  
Petru Jebelean ◽  
Jean Mawhin
Keyword(s):  
Mean Curvature ◽  
Radial Solutions ◽  
Neumann Problems ◽  
Minkowski Spaces

Radial solutions for systems involving mean curvature operators in Euclidean and Minkowski spaces

2009 ◽  
Author(s):  
Cristian Bereanu ◽  
Petru Jebelean ◽  
Jean Mawhin ◽  
Alberto Cabada ◽  
Eduardo Liz ◽  
...  
Keyword(s):  
Mean Curvature ◽  
Radial Solutions ◽  
Minkowski Spaces

scholarly journals A priori bounds and multiplicity of positive solutions for p-Laplacian Neumann problems with sub-critical growth

2019 ◽  
Vol 150 (1) ◽  
pp. 73-102 ◽  
Author(s):  
Alberto Boscaggin ◽  
Francesca Colasuonno ◽  
Benedetta Noris
Keyword(s):  
Positive Solutions ◽  
Critical Power ◽  
A Priori ◽  
Oscillatory Behaviour ◽  
Radial Solutions ◽  
A Priori Bounds ◽  
Shooting Technique ◽  
Neumann Problems ◽  
Multiplicity Of Positive Solutions ◽  
Image Position

AbstractLet 1 < p < +∞ and let Ω ⊂ ℝN be either a ball or an annulus. We continue the analysis started in [Boscaggin, Colasuonno, Noris, ESAIM Control Optim. Calc. Var. (2017)], concerning quasilinear Neumann problems of the type $-\Delta _pu = f(u),\quad u > 0\,{\rm in }\,\Omega ,\quad \partial _\nu u = 0\,{\rm on }\,\partial \Omega .$We suppose that f(0) = f(1) = 0 and that f is negative between the two zeros and positive after. In case Ω is a ball, we also require that f grows less than the Sobolev-critical power at infinity. We prove a priori bounds of radial solutions, focussing in particular on solutions which start above 1. As an application, we use the shooting technique to get existence, multiplicity and oscillatory behaviour (around 1) of non-constant radial solutions.

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