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Existence and iterative construction of solutions for nonlinear Dirichlet elliptic systems involving \((p,q)\)-Laplacian. (English) Zbl 1265.35114

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.

MSC:

35J92 Quasilinear elliptic equations with \(p\)-Laplacian
35J60 Nonlinear elliptic equations
47H05 Monotone operators and generalizations
47J25 Iterative procedures involving nonlinear operators
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