Wei, Li; Liu, Yuanxing; Agarwal, Ravi P. Existence and iterative construction of solutions for nonlinear Dirichlet elliptic systems involving \((p,q)\)-Laplacian. (English) Zbl 1265.35114 Math. Appl. 25, No. 2, 246-252 (2012). Summary: By using the results on the existence of solutions for variational inequalities, we present some abstract results for the existence of the solutions of nonlinear Dirichlet elliptic systems involving \((p, q)\)-Laplacian. By using a result on zero points of maximal monotone operators, we construct an iterative scheme to be convergent strongly to the solutions of the above systems. The systems discussed in this paper and the method used extend and complement some of the previous works. Cited in 2 Documents MSC: 35J92 Quasilinear elliptic equations with \(p\)-Laplacian 35J60 Nonlinear elliptic equations 47H05 Monotone operators and generalizations 47J25 Iterative procedures involving nonlinear operators Keywords:maximal monotone operator; pseudo-monotone operator; \((p,q)\)-Laplacian; zero point; nonlinear Dirichlet elliptic system PDFBibTeX XMLCite \textit{L. Wei} et al., Math. Appl. 25, No. 2, 246--252 (2012; Zbl 1265.35114)