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 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54
  • Publication Date: 2011
  • Doi Number: 10.1017/s0013091509001643
  • Journal Name: PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.345-361
  • Keywords: positive solutions, singular boundary-value problems, existence, uniqueness, dependence, mixed monotone operator, FIXED-POINT THEOREMS, SIGN CHANGING NONLINEARITY, MIXED MONOTONE-OPERATORS, POSITIVE SOLUTIONS, INCREASING HOMEOMORPHISM, P-LAPLACIAN, EXISTENCE, BVP, HOMOMORPHISM
  • Abdullah Gül University Affiliated: No

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.