Search results for "Parametric problem"
showing 3 items of 3 documents
A Parametric Dirichlet Problem for Systems of Quasilinear Elliptic Equations With Gradient Dependence
2016
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.
The effects of convolution and gradient dependence on a parametric Dirichlet problem
2020
Our objective is to study a new type of Dirichlet boundary value problem consisting of a system of equations with parameters, where the reaction terms depend on both the solution and its gradient (i.e., they are convection terms) and incorporate the effects of convolutions. We present results on existence, uniqueness and dependence of solutions with respect to the parameters involving convolutions.
Bounded weak solutions to superlinear Dirichlet double phase problems
2023
AbstractIn this paper we study a Dirichlet double phase problem with a parametric superlinear right-hand side that has subcritical growth. Under very general assumptions on the data, we prove the existence of at least two nontrivial bounded weak solutions to such problem by using variational methods and critical point theory. In contrast to other works we do not need to suppose the Ambrosetti–Rabinowitz condition.