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A priori estimates, existence and non-existence of positive solutions of generalized mean curvature equations
Authors:Qiuyi Dai  Yonggeng Gu  Jiuyi Zhu
Institution:aDepartment of Mathematics, Hunan Normal University, Changsha, Hunan, 410081, China;bDepartment of Mathematics, Wayne State University, Detroit, MI 48202, USA
Abstract:This paper concerns a priori estimates and existence of solutions of generalized mean curvature equations with Dirichlet boundary value conditions in smooth domains. Using the blow-up method with the Liouville-type theorem of the p laplacian equation, we obtain a priori bounds and the estimates of interior gradient for all solutions. The existence of positive solutions is derived by the topological method. We also consider the non-existence of solutions by Pohozaev identities.
Keywords:MSC: 35J60  35B09
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