Existence of triple positive solutions for a third order generalized right focal problem. (English) Zbl 1103.34010

Bai, Zhanbing; Fei, Xiangli

Math. Inequal. Appl. 9, No. 3, 437-444 (2006).

Summary: We obtain sufficient conditions for the existence of at least three positive solutions for the third-order three-point generalized right focal boundary value problem \[ x'''=q(t)f(t,x,x',x''),t_1\leq t\leq t_3, \]
\[ x(t_1)= x'(t_2)=0,\;\eta x(t_3)+\delta x''(t_2)=0, \] where \(f:[t_1,t_3]\times[0, \infty)\times \mathbb{R}^2\to[0, \infty)\), \(q:(t_1,t_3)\to[0,+\infty)\) are nonnegative continuous functions and \(\delta >0\), \(\eta\geq 0\) are constants. This is an application of a new fixed-point theorem introduced by Avery and Peterson.

MSC:

34B18	Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B15	Nonlinear boundary value problems for ordinary differential equations