Maximum principles for fourth order semilinear elliptic boundary value problems

Gajanan C. Lomtea,* and R. M. Dhaigudeb

Maximum principles for fourth order semilinear elliptic boundary value problems

Authors :

Gajanan C. Lomte^a,* and R. M. Dhaigude^b

Author Address :

^aDepartment of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad-431004, India.
^bGovernment Vidarbha Institute of Science and Humanities, Amravati-444 604, Maharashtra, India.

*Corresponding author.

Abstract :

The paper is devoted to prove maximum principles for the certain functionals defined on solution of the fourth order semilinear elliptic equation. The maximum principle so obtained is used to prove the non-existence of nontrivial solutions of the fourth order semilinear elliptic equation with some zero boundary conditions. Hopf’s maximum principle is main ingredient.

Keywords :

Maximum principles, fourth order elliptic equations, integral bounds.

DOI :

Article Info :

Received : October 31, 2012; Accepted : May 05, 2013.