On degree theory for quasilinear elliptic equations with natural growth conditions

2013 ◽  
pp. 1-20 ◽  
Author(s):  
Stefano Almi ◽  
Marco Degiovanni
Keyword(s):  
Elliptic Equations ◽  
Degree Theory ◽  
Growth Conditions ◽  
Quasilinear Elliptic Equations ◽  
Natural Growth ◽  
Quasilinear Elliptic

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 A Fredholm alternative for quasilinear elliptic equations with right-hand side measure

2016 ◽  
Vol 5 (2) ◽  
Author(s):  
Michele Colturato ◽  
Marco Degiovanni
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equation ◽  
Existence Result ◽  
Degree Theory ◽  
Quasilinear Elliptic Equations ◽  
Fredholm Alternative ◽  
Right Hand ◽  
Quasilinear Elliptic

AbstractWe consider a quasilinear elliptic equation with right-hand side measure, which does not satisfy the usual coercivity assumption. We prove an existence result in the line of the Fredholm alternative. For this purpose we develop a variant of degree theory suited to this setting.

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.

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