Electron. J. Diff. Equ., Vol. 2013 (2013), No. 144, pp. 1-14.

Multiple solutions for a quasilinear (p,q)-elliptic system

Seyyed Mohsen Khalkhali, Abdolrahman Razani

We prove the existence of three weak solutions of a quasilinear elliptic system involving a general (p,q)-elliptic operator in divergence form, with $1<p\leq n$, $1<q\leq n$. Our main tool is an adaptation of a three critical points theorem due to Ricceri.

Submitted May 8, 2013. Published June 25, 2013.
Math Subject Classifications: 35J50, 35D30, 35J62, 35J92, 49J35.
Key Words: Weak solutions; critical points; Dirichlet system; divergence type operator.

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Seyyed Mohsen Khalkhali
Department of Mathematics, Science and Research branch
Islamic Azad University, Tehran, Iran
email: sm.khalkhali@srbiau.ac.ir
Abdolrahman Razani
Department of Mathematics
Imam Khomeini International University
Qazvin, Iran
email: razani@ikiu.ac.ir

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