Nonlinear Systems of Elliptic Equations with Natural Growth Conditions and Sign Conditions

2002 ◽  
Vol 46 (2) ◽  
pp. 143-166 ◽  
Author(s):  
Bensoussan Alain ◽  
Boccardo Lucio
Keyword(s):  
Nonlinear Systems ◽  
Elliptic Equations ◽  
Growth Conditions ◽  
Natural Growth ◽  
Systems Of Elliptic Equations ◽  
Sign Conditions

On the Solvability of Some Nonlinear Systems of Elliptic Equations

2001 ◽  
Vol 1 (2) ◽  
Author(s):  
A.M. Piccirillo ◽  
L. Toscano ◽  
S. Toscano
Keyword(s):  
Nonlinear Systems ◽  
Elliptic Equations ◽  
Multiple Solutions ◽  
Systems Of Elliptic Equations

AbstractWe study the solvability and the existence of multiple solutions of nonlinear systems of elliptic equations.

Bifurcation for quasilinear elliptic equations on Rn with natural growth conditions

1989 ◽  
Vol 113 (3-4) ◽  
pp. 215-228 ◽  
Author(s):  
Cao Daomin ◽  
Li Gongbao ◽  
Yan Shusen
Keyword(s):  
Eigenvalue Problem ◽  
Elliptic Equations ◽  
Growth Conditions ◽  
Quasilinear Elliptic Equations ◽  
Natural Growth ◽  
Image Position ◽  
Quasilinear Elliptic

SynopsisWe consider the following eigenvalue problem:We prove the existence of H1(Rn)∩L∞(Rn) bifurcation at λ=0 but only require aij(x, t) (i,j= 1, 2, …,n) and f(x, t) to satisfy certain conditions in theneighbourhood of Rn × {0}.

scholarly journals Existence of Solutions for Unbounded Elliptic Equations with Critical Natural Growth

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Aziz Bouhlal ◽  
Abderrahmane El Hachimi ◽  
Jaouad Igbida ◽  
El Mostafa Sadek ◽  
Hamad Talibi Alaoui
Keyword(s):  
Elliptic Problem ◽  
Lebesgue Space ◽  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Regularity Of Solutions ◽  
Natural Growth ◽  
Existence And Regularity Results ◽  
Regularity Results

We investigate existence and regularity of solutions to unbounded elliptic problem whose simplest model is {-div[(1+uq)∇u]+u=γ∇u2/1+u1-q+f  in  Ω,  u=0  on  ∂Ω,}, where 0<q<1, γ>0 and f belongs to some appropriate Lebesgue space. We give assumptions on f with respect to q and γ to show the existence and regularity results for the solutions of previous equation.

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