Positive Solutions to Nonlinear First-Order Nonlocal BVPs with Parameter on Time Scales

• Main Authors: Luo Hua, Gao Chenghua
• Format: Article
• Language: English
• Published: SpringerOpen 2011-01-01
• Series: Boundary Value Problems
• Online Access: http://www.boundaryvalueproblems.com/content/2011/198598

<p/> <p>We discuss the existence of solutions for the first-order multipoint BVPs on time scale <inline-formula> <graphic file="1687-2770-2011-198598-i1.gif"/></inline-formula>: <inline-formula> <graphic file="1687-2770-2011-198598-i2.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2011-198598-i3.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2011-198598-i4.gif"/></inline-formula>, where <inline-formula> <graphic file="1687-2770-2011-198598-i5.gif"/></inline-formula> is a parameter, <inline-formula> <graphic file="1687-2770-2011-198598-i6.gif"/></inline-formula> is a fixed number, <inline-formula> <graphic file="1687-2770-2011-198598-i7.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2011-198598-i8.gif"/></inline-formula> is continuous, <inline-formula> <graphic file="1687-2770-2011-198598-i9.gif"/></inline-formula> is regressive and rd-continuous, <inline-formula> <graphic file="1687-2770-2011-198598-i10.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2011-198598-i11.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2011-198598-i12.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2011-198598-i13.gif"/></inline-formula>, and <inline-formula> <graphic file="1687-2770-2011-198598-i14.gif"/></inline-formula>. For suitable <inline-formula> <graphic file="1687-2770-2011-198598-i15.gif"/></inline-formula>, some existence, multiplicity, and nonexistence criteria of positive solutions are established by using well-known results from the fixed-point index.</p>