New Positive Solutions of Nonlinear Elliptic PDEs

• Main Authors: Mustafa Inc, Noureddine Bouteraa, Mehmet Ali Akinlar, Slimane Benaicha, Yu-Ming Chu, Gerhard-Wilhelm Weber, Bandar Almohsen
• Format: Article
• Language: English
• Published: MDPI AG 2020-07-01
• Series: Applied Sciences
• Subjects: positive (global) solution; (strict) upper and lower solutions; multiplicity of positive solutions; elliptic BVPs
• Online Access: https://www.mdpi.com/2076-3417/10/14/4863

We are concerned with positive solutions of two types of nonlinear elliptic boundary value problems (BVPs). We present conditions for existence, uniqueness and multiple positive solutions of a first type of elliptic BVPs. For a second type of elliptic BVPs, we obtain conditions for existence and uniqueness of positive global solutions. We employ mathematical tools including strictly upper (SU) and strictly lower (SL) solutions, iterative sequence method and Amann theorem. We present our research findings in new original theorems. Finally, we summarize and indicate areas of future study and possible applications of the research work.