×

Multiple positive solutions of fourth-order boundary value problems. (English) Zbl 1071.34025

Summary: We discuss the existence of multiple positive solutions for the fourth-order boundary value problem \[ u^{(4)}(t)+\beta u''(t)= f(t, u(t)),\quad 0< t< 1,\quad u(0)= u(1)= u''(0)= u''(1)= 0, \] where \(f: [0,1]\times [0,\infty)\to [0,\infty)\) is continuous and \(\beta< \pi^2\). Existence is established via the theory of fixed-point index in cones.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI