The aim of this article is to study the Dirichlet boundary value problem for systems of equations involving the (pi, qi) -Laplacian operators and parameters μi≥0 (i = 1,2) in the principal part. Another main point is that the nonlinearities in the reaction terms are allowed to depend on both the solution and its gradient. We prove results ensuring existence, uniqueness, and asymptotic behavior with respect to the parameters.
Motreanu, D., Vetro, C., Vetro, F. (2016). A Parametric Dirichlet Problem for Systems of Quasilinear Elliptic Equations With Gradient Dependence. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 37(12), 1551-1561 [10.1080/01630563.2016.1219866].
A Parametric Dirichlet Problem for Systems of Quasilinear Elliptic Equations With Gradient Dependence
VETRO, Calogero;VETRO, Francesca
2016-01-01
Abstract
The aim of this article is to study the Dirichlet boundary value problem for systems of equations involving the (pi, qi) -Laplacian operators and parameters μi≥0 (i = 1,2) in the principal part. Another main point is that the nonlinearities in the reaction terms are allowed to depend on both the solution and its gradient. We prove results ensuring existence, uniqueness, and asymptotic behavior with respect to the parameters.
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