Minimax Theory and its Applications 06 (2021), No. 1, 155--172
Copyright Heldermann Verlag 2021
On the Sub-Supersolution 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 super-solution 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, sub-supersolution, positive solution.
MSC: 35J62.
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