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Authors: DUMITRU MOTREANU, VIORICA VENERA MOTREANU.
DOI: 10.24193/subbmath.2021.1.08
Published Online: 2021-03-20
Published Print: 2021-03-30
pp. 95-103
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ABSTRACT.
The paper focuses on a nonstandard Dirichlet problem driven by the operator $-Delta_p +muDelta_q$, which is a competing $(p,q)$-Laplacian with lack of ellipticity if $mu>0$, and exhibiting a reaction term in the form of a convection (i.e., it depends on the solution and its gradient) composed with the convolution of the solution with an integrable function. We prove the existence of a generalized solution through a combination of fixed-point approach and approximation. In the case $muleq 0$, we obtain the existence of a weak solution to the respective elliptic problem.
Mathematics Subject Classification (2010): 35J92, 47H30.
Keywords: Competing (p; q)-Laplacian, Dirichlet problem, convection, convolution, generalized solution, weak solution.
