Electron.n. J. Diff. Eqns., Vol. 1999(1999), No. 14, pp. 1-12.

Existence of multiple solutions for quasilinear diagonal elliptic systems

Marco Squassina

Abstract:
Nonsmooth-critical-point theory is applied in proving multiplicity results for the quasilinear symmetric elliptic system
$$ -\sum_{i,j=1}^{n}D_j(a^{k}_{ij}(x,u)D_iu_k)+ {1\over 2}\sum_{i,j=1}^{n}\sum_{h=1}^N D_{s_k}a^{h}_{ij}(x,u)D_iu_hD_ju_h=g_k(x,u)\,, $$
for $k=1,..,N$.

Submitted January 4, 1999. Published May 10, 1999.
Math Subject Classification: 35D05, 35J20, 35J60.
Key Words: Quasilinear elliptic differential systems, Nonsmooth critical point theory.

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Marco Squassina
Dipartimento di Matematica, Milan University
Via Saldini 50, 20133 Milano, Italy
e-mail: squassin@ares.mat.unimi.it
http://www.dmf.bs.unicatt.it/~squassin

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