Fixed point theorems for mixed monotone vector operators with application to systems of nonlinear boundary value problems. (English) Zbl 1482.54080
Summary: In this paper, we present and prove new existence and uniqueness fixed point theorems for vector operators having a mixed monotone property in partially ordered product Banach spaces. Our results extend and improve existing works on \(\tau\)-\(\varphi \)-concave operators in the scalar case. As an application, we study the existence and uniqueness of positive solutions for systems of nonlinear Neumann boundary value problems.
MSC:
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 47H10 | Fixed-point theorems |
| 54E50 | Complete metric spaces |
| 34B18 | Positive solutions to nonlinear boundary value problems for ordinary differential equations |
Keywords:
fixed point in product cone; mixed monotone vector operators; systems of boundary value problemsReferences:
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