The behavior of bounded solutions of quasilinear elliptic equations on manifolds

2009 ◽  
Vol 86 (1-2) ◽  
pp. 53-64
Author(s):  
A. B. Ivanov
Keyword(s):  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Bounded Solutions ◽  
Quasilinear Elliptic

scholarly journals Quasilinear Dirichlet Problems with Degenerated p-Laplacian and Convection Term

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 139
Author(s):  
Dumitru Motreanu ◽  
Elisabetta Tornatore
Keyword(s):  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Convection Term ◽  
Bounded Solutions ◽  
Dirichlet Problems ◽  
Abstract Result ◽  
Functional Setting ◽  
Quasilinear Elliptic ◽  
Substantial Change

The paper develops a sub-supersolution approach for quasilinear elliptic equations driven by degenerated p-Laplacian and containing a convection term. The presence of the degenerated operator forces a substantial change to the functional setting of previous works. The existence and location of solutions through a sub-supersolution is established. The abstract result is applied to find nontrivial, nonnegative and bounded solutions.

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