Electron. J. Differential Equations, Vol. 2019 (2019), No. 57, pp. 1-13.

Nonlinear Dirichlet problems with the combined effects of singular and convection terms

Yunru Bai, Leszek Gasinski, Nikolaos S. Papageorgiou

We consider a nonlinear Dirichlet elliptic problem driven by the p-Laplacian. In the reaction term of the equation we have the combined effects of a singular term and a convection term. Using a topological approach based on the fixed point theory (the Leray-Schauder alternative principle), we prove the existence of a positive smooth solution.

Submitted November 12, 2018. Published May 3, 2019.
Math Subject Classifications: 35J92, 35P30.
Key Words: Singular term; convection term; strong comparison; Leray-Schauder alternative principle.

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Yunru Bai
Jagiellonian University
Faculty of Mathematics and Computer Science
ul. Lojasiewicza 6
30-348 Krakow, Poland
email: yunrubai@163.com
Leszek Gasinski
Department of Mathematics
Pedagogical University of Cracow
Podchorazych 2, 30-084 Cracow, Poland
email: leszek.gasinski@up.krakow.pl
Nikolaos S. Papageorgiou
National Technical University
Department of Mathematics, Zografou Campus
Athens 15780, Greece
email: npapg@math.ntua.gr

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