Three solutions for a class of quasilinear elliptic systems in Orlicz–Sobolev spaces

Abstract

We study the solutions of the Neumann problem for a class of elliptic partial differential systems on a bounded domain and obtain three solutions under appropriate hypotheses. Our technical approach is based on the general three critical point theorem obtained by B. Ricceri in Orlicz–Sobolev spaces.

Keywords:

• nonhomogeneous differential operator
• nonlinear eigenvalue problem
• Orlicz–Sobolev space

AMS Subject Classifications::

• 35D05
• 35J60
• 35J70
• 58E05
• 46N20