Graef, John R.; Yang, Bo Existence and nonexistence of positive solutions of fourth order nonlinear boundary value problems. (English) Zbl 1031.34025 Appl. Anal. 74, No. 1-2, 201-214 (2000). Summary: The authors consider boundary value problems for fourth-order ordinary differential equations of the form \[ u''''(t)= \lambda a(t)f(u),\;0<t<1,\tag{E} \] with the boundary conditions \[ u(0)=u'(1)= u''(0)= u'''(1)=0,\text{ or}\tag \(B_1\) \]\[ u(0)=u'(1)=u''(1)=u'''(0)=0.\tag \( B_2\) \] They give sufficient conditions for problems (E)–(B\(_1)\) and (E)-(B\(_2)\) to have at least one positive solution. They also give sufficient conditions for these problems to have no positive solutions. Examples to illustrate that the results are sharp are also included. Cited in 2 ReviewsCited in 35 Documents MSC: 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:boundary value problems; fourth-order ordinary differential equations PDFBibTeX XMLCite \textit{J. R. Graef} and \textit{B. Yang}, Appl. Anal. 74, No. 1--2, 201--214 (2000; Zbl 1031.34025) Full Text: DOI