- Publication venue
- University of Szeged, Hungary
- Publication date
- 01/01/2010
- Field of study
Get PDFIn this paper, we consider the existence of multiple positive solutions for the 2n-th order m-point boundary value problems:
β©β¨β§βx(2n)(t)=f(t,x(t),xβ²β²(t),β―,x(2(nβ1))(t)),0β€tβ€1,x(2i+1)(0)=j=1βmβ2βΞ±ijβx(2i+1)(ΞΎjβ),x(2i)(1)=j=1βmβ2βΞ²ijβx(2i)(ΞΎjβ),0β€iβ€nβ1,β
where Ξ±ijβ,Ξ²ijβΒ (0β€iβ€nβ1,1β€jβ€mβ2)β[0,β), j=1βmβ2βΞ±ijβ,j=1βmβ2βΞ²ijββ(0,1), 0<ΞΎ1β<ΞΎ2β<β¦<ΞΎmβ2β<1. Using Leggett-Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem