
Minimax Theory and its Applications 06 (2021), No. 1, 155172 Copyright Heldermann Verlag 2021 On the SubSupersolution Approach for Dirichlet Problems driven by a (p(x),q(x))Laplacian Operator with Convection Term Antonia Chinni Department of Engineering, University of Messina, Italy achinni@unime.it Angela Sciammetta Department of Mathematics and Computer Science, University of Palermo, Italy angela.sciammetta@unipa.it Elisabetta Tornatore Department of Mathematics and Computer Science, University of Palermo, Italy elisa.tornatore@unipa.it The method of sub and supersolution is applied to obtain existence and location of solutions to a quasilinear elliptic problem with variable exponent and Dirichlet boundary conditions involving a nonlinear term f depending on solution and on its gradient. Under a suitable growth condition on the convection term f, the existence of at least one solution satisfying a priori estimate is obtained. Keywords: (p(x),q(x))Laplacian, Dirichlet problem, gradient dependence, subsupersolution, positive solution. MSC: 35J62. [ Fulltextpdf (149 KB)] for subscribers only. 