Existence of Positive Solutions to a Nonlocal Boundary Value Problem with <inline-formula><graphic file="1687-1847-2010-809497-i1.gif"/></inline-formula>-Laplacian onTime Scales

oleh: Sun Ting-Ting, Wang Lin-Lin, Fan Yong-Hong

Format: Article
Diterbitkan: SpringerOpen 2010-01-01

Deskripsi

<p/> <p>The nonlocal boundary value problem, with <inline-formula><graphic file="1687-1847-2010-809497-i2.gif"/></inline-formula>-Laplacian of the form <inline-formula><graphic file="1687-1847-2010-809497-i3.gif"/></inline-formula><inline-formula><graphic file="1687-1847-2010-809497-i4.gif"/></inline-formula>, has been considered. Two existence criteria of at least one and three positive solutions are presented. The first one is based on the Four functionals fixed point theorem in the work of R. Avery et al. (2008), and the second one is based on the Five functionals fixed point theorem. Meanwhile an example is worked out to illustrate the main result.</p>