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We consider the nonlinear fourth-order semipositone boundary value problem $$\begin{aligned} u^{(4)}=f(t,u(t),u'(t)), \quad t \in (0,1), \end{aligned}$$u(4)=f(t,u(t),u′(t)),t∈(0,1),$$\begin{aligned} u(0)=u'(0)=u''(1)=u'''(1)=0, \end{aligned}$$u(0)=u′(0)=u′′(1)=u′′′(1)=0,where $$f: [0,1] \times [0,\infty ) \times [0, \infty ) \rightarrow (-\infty ,… Click to show full abstract
We consider the nonlinear fourth-order semipositone boundary value problem $$\begin{aligned} u^{(4)}=f(t,u(t),u'(t)), \quad t \in (0,1), \end{aligned}$$u(4)=f(t,u(t),u′(t)),t∈(0,1),$$\begin{aligned} u(0)=u'(0)=u''(1)=u'''(1)=0, \end{aligned}$$u(0)=u′(0)=u′′(1)=u′′′(1)=0,where $$f: [0,1] \times [0,\infty ) \times [0, \infty ) \rightarrow (-\infty , \infty )$$f:[0,1]×[0,∞)×[0,∞)→(-∞,∞) has the property $$f(t,x,y) \ge -g(t)$$f(t,x,y)≥-g(t) for a nonnegative continuous function g(t). This paper improves the results of Ma (Hiroshima Math J 33:217–227, 2013) and Spraker (Differ Equ Appl 8:21–31, 2016).
Journal Title: Mediterranean Journal of Mathematics
Year Published: 2017
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