scholarly journals Finite energy solutions of quasilinear elliptic equations with sub-natural growth terms

2014 ◽  
Vol 52 (3-4) ◽  
pp. 529-546 ◽  
Author(s):  
Cao Tien Dat ◽  
Igor E. Verbitsky
Keyword(s):  
Elliptic Equations ◽  
Finite Energy ◽  
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.

scholarly journals Quasilinear elliptic equations with sub-natural growth and nonlinar potentials

2015 ◽  
Author(s):  
◽  
Dat Tien Cao
Keyword(s):  
Sufficient Conditions ◽  
Finite Energy ◽  
Quasilinear Elliptic Equations ◽  
Natural Growth ◽  
Estimates Of Solutions ◽  
Regularity Properties ◽  
Nonlinear Potentials ◽  
Necessary And Sufficient ◽  
Quasilinear Elliptic

Necessary and sufficient conditions for the existence of finite energy and weak solutions are given. Sharp global pointwise estimates of solutions are obtained as well. We also discuss the uniqueness and regularity properties of solutions. As a consequence, characterization of solvability of the equations with singular natural growth in the gradient terms is deduced. Our main tools are Wolff potential estimates, dyadic models, and related integral inequalities. Special nonlinear potentials of Wolff type ssociated with "sublinear" problems are constructed to obtain sharp bounds of solutions. We also treat equations with the fractional Laplacians. Our approach is applicable to more general quasilinear A-Laplace operators as well as the fully nonlinear k-Hessian operators.

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}.

Sign in / Sign up

Export Citation Format

Share Document