Aboubacar Abdou, Aboubacar Marcos
Abstract:
In this article we study the existence of solutions for the
Dirichlet problem
where
is a smooth bounded domain in
,
V is a given function in a generalized Lebesgue space
and f(x,u) is a Caratheodory function which satisfies some growth condition.
Using variational arguments based on "Fountain theorem"
and "Dual Fountain theorem", we shall prove under appropriate conditions on
the above nonhomogeneous quasilinear problem the existence of two sequences of
weak solutions for this problem.
Submitted December 18, 2015. Published July 24, 2016.
Math Subject Classifications: 35B38, 35J20, 35J60, 35J66, 58E05.
Key Words: p(x)-Laplacian operator; generalized Lebesgue-Sobolev spaces;
critical point; Fountain theorem; dual Fountain theorem.
Show me the PDF file (298 KB), TEX file for this article.
Aboubacar Abdou Institut de Mathématiques et de Sciences Physiques Université d'Abomey Calavi, 01 BP: 613 Porto-Novo, Bénin email: aboubacar.abdou@imsp-uac.org, abdou.aboubacar@ymail.com | |
Aboubacar Marcos Institut de Mathématiques et de Sciences Physiques Université d'Abomey Calavi, 01 BP: 613 Porto-Novo, Bénin email: abmarcos@imsp-uac.org, abmarcos@yahoo.fr |
Return to the EJDE web page