HIGHER-ORDER SINGULAR MULTI-POINT BOUNDARY-VALUE PROBLEMS ON TIME SCALES


DOĞAN A. , Graef J. R. , Kong L.

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, vol.54, pp.345-361, 2011 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54
  • Publication Date: 2011
  • Doi Number: 10.1017/s0013091509001643
  • Title of Journal : PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY
  • Page Numbers: pp.345-361

Abstract

We study classes of higher-order singular boundary-value problems on a time scale T with a positive parameter lambda in the differential equations. A homeomorphism and homomorphism phi are involved both in the differential equation and in the boundary conditions. Criteria are obtained for the existence and uniqueness of positive solutions. The dependence of positive solutions on the parameter lambda is studied. Applications of our results to special problems are also discussed. Our analysis mainly relies on the mixed monotone operator theory. The results here are new, even in the cases of second-order differential and difference equations.