New Positive Solutions of Nonlinear Elliptic PDEs

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 uni...

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Bibliographic Details
Published in:Applied sciences 2020-07, Vol.10 (14), p.4863
Main Authors: Inc, Mustafa, Bouteraa, Noureddine, Akinlar, Mehmet Ali, Benaicha, Slimane, Chu, Yu-Ming, Weber, Gerhard-Wilhelm, Almohsen, Bandar
Format: Article
Language:English
Subjects:
(strict) upper and lower solutions
Analysis
Boundary value problems
Differential equations, Nonlinear
Differential equations, Partial
elliptic BVPs
Methods
multiplicity of positive solutions
positive (global) solution
Problem solving
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Summary: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.
ISSN:2076-3417
2076-3417
DOI:10.3390/app10144863