WE PROVE THE EXISTENCE OF AT LEAST TWO POSITIVE SOLUTIONS FOR THE LAPLACIAN SYSTEM (FORMULA) ON A BOUNDED REGION W BY USING THE NEHARI MANIFOLD AND THE FIBERING MAPS ASSOCIATED WITH THE EULER FUNCTIONAL FOR THE SYSTEM.

THIS PAPER DEALS WITH THE EXISTENCE OF POSITIVE WEAK SOLUTIONS FOR A CLASS OF P-BIHARMONIC ELLIPTIC PROBLEMS WITH DIRICHLET BOUNDARY CONDITIONS IN AN EXTERIOR DO-MAIN. BY THE VARIATIONAL PRINCIPLE AND THE MOUNTAIN PASS LEMMA, THE EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A CLASS OF P-BIHARMONIC ELLIPTIC EXTERIOR PROBLEMS ARE OBTAINED.

THIS PAPER CONSIDERS THE EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF QUASILINEAR ELLIPTIC SYSTEMS WITH NONLINEAR BOUNDARY CONDITIONS. BY USING THE FIBERING METHOD, WE PROVE THAT THERE EXISTS L*>0 SUCH THAT FOR 0<L<L*, THE GIVEN PROBLEM HAS AT LEAST TWO POSITIVE SOLUTIONS.

THE MULTIPLICITY OF POSITIVE SOLUTIONS FOR PROBLEM (FORMULA) IS DISCUSSED. THIS INVESTIGATION IS BASED ON NEHARI MANIFOLD TECHNIQUE AND VARIATIONAL ARGUMENT.