Existence of solutions for non-uniformly nonlinear elliptic systems

Existence of solutions for non-uniformly nonlinear elliptic systems

Using a variational approach, we prove the existence of solutions for the degenerate quasilinear elliptic system $$displaylines{ -hbox{div}(u_1 (x)|abla u|^{p-2} abla u) =lambda F_u(x,u,v)+mu G_u(x,u,v),cr -hbox{div}(u_2 (x)|abla v|^{q-2} abla v) =lambda F_v(x,u,v)+mu G_v(x,u,v), }$$ with Di...

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Main Authors: Ghasem Alizadeh Afrouzi, Somayeh Mahdavi, Nikolaos B. Zographopoulos
Format: Article
Language:English
Published: Texas State University 2011-12-01
Series:Electronic Journal of Differential Equations
Subjects:
Non-uniformly elliptic system
mountain pass theorem
minimum principle
Online Access:http://ejde.math.txstate.edu/Volumes/2011/167/abstr.html
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spelling doaj-1e0e74941d934db597a026b752a5144e2020-11-24T23:09:02ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912011-12-012011167,19Existence of solutions for non-uniformly nonlinear elliptic systemsGhasem Alizadeh AfrouziSomayeh MahdaviNikolaos B. ZographopoulosUsing a variational approach, we prove the existence of solutions for the degenerate quasilinear elliptic system $$displaylines{ -hbox{div}(u_1 (x)|abla u|^{p-2} abla u) =lambda F_u(x,u,v)+mu G_u(x,u,v),cr -hbox{div}(u_2 (x)|abla v|^{q-2} abla v) =lambda F_v(x,u,v)+mu G_v(x,u,v), }$$ with Dirichlet boundary conditions. http://ejde.math.txstate.edu/Volumes/2011/167/abstr.htmlNon-uniformly elliptic systemmountain pass theoremminimum principle
collection DOAJ
language English
format Article
sources DOAJ
author Ghasem Alizadeh Afrouzi
Somayeh Mahdavi
Nikolaos B. Zographopoulos
spellingShingle Ghasem Alizadeh Afrouzi
Somayeh Mahdavi
Nikolaos B. Zographopoulos
Existence of solutions for non-uniformly nonlinear elliptic systems
Electronic Journal of Differential Equations
Non-uniformly elliptic system
mountain pass theorem
minimum principle
author_facet Ghasem Alizadeh Afrouzi
Somayeh Mahdavi
Nikolaos B. Zographopoulos
author_sort Ghasem Alizadeh Afrouzi
title Existence of solutions for non-uniformly nonlinear elliptic systems
title_short Existence of solutions for non-uniformly nonlinear elliptic systems
title_full Existence of solutions for non-uniformly nonlinear elliptic systems
title_fullStr Existence of solutions for non-uniformly nonlinear elliptic systems
title_full_unstemmed Existence of solutions for non-uniformly nonlinear elliptic systems
title_sort existence of solutions for non-uniformly nonlinear elliptic systems
publisher Texas State University
series Electronic Journal of Differential Equations
issn 1072-6691
publishDate 2011-12-01
description Using a variational approach, we prove the existence of solutions for the degenerate quasilinear elliptic system $$displaylines{ -hbox{div}(u_1 (x)|abla u|^{p-2} abla u) =lambda F_u(x,u,v)+mu G_u(x,u,v),cr -hbox{div}(u_2 (x)|abla v|^{q-2} abla v) =lambda F_v(x,u,v)+mu G_v(x,u,v), }$$ with Dirichlet boundary conditions.
topic Non-uniformly elliptic system
mountain pass theorem
minimum principle
url http://ejde.math.txstate.edu/Volumes/2011/167/abstr.html
work_keys_str_mv AT ghasemalizadehafrouzi existenceofsolutionsfornonuniformlynonlinearellipticsystems
AT somayehmahdavi existenceofsolutionsfornonuniformlynonlinearellipticsystems
AT nikolaosbzographopoulos existenceofsolutionsfornonuniformlynonlinearellipticsystems
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