Infinite many positive solutions for nonlinear first-order BVPs with integral boundary conditions on time scales
Keywords
Time scale, boundary value problem, positive solution, integral boundary conditionAbstract
In this paper, we investigate the existence of infinite many positive solutions for the nonlinear first-order BVP with integral boundary conditions $$ \cases x^{\Delta}(t)+p(t)x^{\sigma}(t)=f(t,x^{\sigma}(t)), & t\in (0,T)_{\mathbb{T}}, \\ x(0)-\beta x^{\sigma}(T)=\alpha\int_{0}^{\sigma(T)}x^{\sigma}(s)\Delta g(s), \endcases $$ 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 $\mathbb{T}$.Downloads
Published
2013-04-22
How to Cite
1.
LI, Yongkun and SUN, Lijuan. Infinite many positive solutions for nonlinear first-order BVPs with integral boundary conditions on time scales. Topological Methods in Nonlinear Analysis. Online. 22 April 2013. Vol. 41, no. 2, pp. 305 - 321. [Accessed 20 April 2024].
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