Existence of multiple solutions for quasilinear diagonal elliptic systems

Abstract

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

Keywords

• Quasilinear elliptic differential systems
• Nonsmooth critical point theory.