Topological Methods in Nonlinear Analysis

Infinite many positive solutions for nonlinear first-order BVPs with integral boundary conditions on time scales

Yongkun Li and Lijuan Sun

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Abstract

In this paper, we investigate the existence of infinite many positive solutions for the nonlinear first-order BVP with integral boundary conditions $$ \begin{cases} x^{\Delta}(t)+p(t)x^{\sigma}(t)=f(t,x^{\sigma}(t)), & t\in (0,T)_{\mathbb{T}}, \\ x(0)-\beta x^{\sigma}(T)=\alpha\int_{0}^{\sigma(T)}x^{\sigma}(s)\Delta g(s), \end{cases} $$ where $x^{\sigma}=x\circ\sigma$, $f\colon [0,T]_{\mathbb{T}}\times\mathbb{R^{+}}\rightarrow\mathbb{R^{+}}$ is continuous, $p$ is regressive and rd-continuous, $\alpha,\beta\geq0$, $g\colon [0,T]_{\mathbb{T}}\rightarrow \mathbb{R}$ is a nondecreasing function. By using the fixed-point index theory and a new fixed point theorem in a cone, we provide sufficient conditions for the existence of infinite many positive solutions to the above boundary value problem on time scale $\mathbb{T}$.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 41, Number 2 (2013), 305-321.

Dates
First available in Project Euclid: 21 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1461245480

Mathematical Reviews number (MathSciNet)
MR3114310

Zentralblatt MATH identifier
1292.34088

Citation

Li, Yongkun; Sun, Lijuan. Infinite many positive solutions for nonlinear first-order BVPs with integral boundary conditions on time scales. Topol. Methods Nonlinear Anal. 41 (2013), no. 2, 305--321. https://projecteuclid.org/euclid.tmna/1461245480


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Nicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies

Topological Methods in Nonlinear Analysis

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