Existence of three positive solutions for some second-order boundary value problems

✍ Scribed by Zhanbing Bai; Weigao Ge

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 420 KB
• Volume: 48
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2004.03.002

✦ Synopsis

In this paper, a new fixed-point theorem of functional type in a cone is established. With using the new fixed-point theorem and imposing growth conditions on the nonlinearity, the existence of three positive solutions for the boundary value problem

x"(O+f(t,x(t),x'(t))=O , 0<t<l, x(0) = x(1) = 0, is obtained. Here f : [0, 1] x [0, oo) x R ~ [0, oo) is continuous. Finally, an example is given to illustrate the importance of results obtained.