Abstract
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.
Highlights
Nonlinear elliptic boundary value problems (NEBVP) are significantly important type PDEs having applications in different branches of science and engineering including fluid mechanics such as exothermic chemical reactions or auto catalytic reactions, see [1], in physics and chemistry
By employing Amann Theorem [31], we show multiple positive solutions
We are interested in existence of global solutions of (2)
Summary
Nonlinear elliptic boundary value problems (NEBVP) are significantly important type PDEs having applications in different branches of science and engineering including fluid mechanics such as exothermic chemical reactions or auto catalytic reactions, see [1], in physics and chemistry. The main scope of these papers consists in the imposing some conditions on the nonlinearity c (c is the data) to prove the existence solutions to the problem (1) in smooth domains in the presence of well-ordered lower and upper solutions.
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