The Fatou lemma approach to the existence in quasilinear elliptic equations with natural growth terms

2010 ◽  
Vol 55 (5-6) ◽  
pp. 445-453 ◽  
Author(s):  
Lucio Boccardo
Keyword(s):  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Natural Growth ◽  
Natural Growth Terms ◽  
Quasilinear Elliptic

Strong Maximum Principle for Some Quasilinear Dirichlet Problems Having Natural Growth Terms

2020 ◽  
Vol 20 (2) ◽  
pp. 503-510
Author(s):  
Lucio Boccardo ◽  
Luigi Orsina
Keyword(s):  
Maximum Principle ◽  
Elliptic Equations ◽  
Strong Maximum Principle ◽  
Quasilinear Elliptic Equations ◽  
Quadratic Growth ◽  
Natural Growth ◽  
Dirichlet Problems ◽  
Natural Growth Terms ◽  
Quasilinear Elliptic ◽  
Lower Order Terms

AbstractIn this paper, dedicated to Laurent Veron, we prove that the Strong Maximum Principle holds for solutions of some quasilinear elliptic equations having lower order terms with quadratic growth with respect to the gradient of the solution.

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}.

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