Fixed point theorems in ordered metric spaces and applications to nonlinear boundary value problems


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	Fixed point theorems in ordered metric spaces and applications to nonlinear boundary value problems


	Fixed Point Theory, Volume 20, No. 1, 2019, 349-364, February 1st, 2019 DOI: 10.24193/fpt-ro.2019.1.23 Authors: Toshikazu Watanabe Abstract: In this paper, we extend the concept of mixed monotone mappings and then we consider certain fixed point theorems for a pair of mappings in metric spaces with a partial ordering. As an application, we study existence of solutions for the following fourth-order two-point boundary value problems for elastic beam equations: $\begin{cases}u^{\prime\prime\prime\prime}(t)=f(t,u(t),u^{\prime\prime}(t)),\medskip \\ u(0)=A, u^{\prime}(0)=B, u^{\prime\prime}(1)=C, u^{\prime\prime\prime}(1)=D, \end{cases}$ where ƒ is a continuous mapping of [0,1] × ℝ × ℝ into ℝ. Moreover, using these fixed point theorems, we prove several existence results forthe solutions of various boundary value problems. Key Words and Phrases: Fixed point theorem, partially ordered set, boundary value problem, differential equation. 2010 Mathematics Subject Classification: 34B99, 47H10, 54H25. Published on-line: February 1st, 2019. Abstract pdf Fulltext pdf Back to volume's table of contents