Electron. J. Differential Equations, Vol. 2018 (2018), No. 101, pp. 1-18.

Existence of solutions to nonhomogeneous Dirichlet problems with dependence on the gradient

Yunru Bai

The goal of this article is to explore the existence of positive solutions for a nonlinear elliptic equation driven by a nonhomogeneous partial differential operator with Dirichlet boundary condition. This equation a convection term and thereaction term is not required to satisfy global growth conditions. Our approach is based on the Leray-Schauder alternative principle, truncation and comparison approaches, and nonlinear regularity theory.

Submitted December 8, 2017. Published May 2, 2018.
Math Subject Classifications: 35J92, 35P30.
Key Words: Nonhomogeneous p-Laplacian operator; nonlinear regularity; Dirichlet boundary condition; convection term; truncation; Leray-Schauder alternative.

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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

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