Bai, Yunru2022-02-022022-02-022018-05-02Bai, Y. (2018). Existence of solutions to nonhomogeneous Dirichlet problems with dependence on the gradient. <i>Electronic Journal of Differential Equations, 2018</i>(101), pp. 1-18.1072-6691https://hdl.handle.net/10877/15268The 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.Text18 pages1 file (.pdf)enAttribution 4.0 InternationalNonhomogeneous p-Laplacian operatorNonlinear regularityDirichlet boundary conditionConvection termTruncationLeray-Schauder alternativeArticle