Abstract
In this paper, we study the existence and uniqueness of positive solutions for a class of nonlinear operator equations on ordered Banach spaces. Various applications are also considered to illustrate our obtained results (existence of solutions to quadratic integral equations with a linear modification of the argument, positive solution of second-order Neumann boundary value problem, and positive definite solutions of a class of nonlinear matrix equations).
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Berzig, M., Samet, B. Positive fixed points for a class of nonlinear operators and applications. Positivity 17, 235–255 (2013). https://doi.org/10.1007/s11117-012-0162-z
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DOI: https://doi.org/10.1007/s11117-012-0162-z
Keywords
- Operator equation Banach space
- Normal cone
- Positive solution
- Fixed point
- Integral equation
- Boundary values problem
- Nonlinear matrix equation