Positive Solutions of Higher-Order Boundary-Value Problems

Kong, Lingju; Kong, Qingkai

doi:10.1017/s0013091504000860

Cited by 17 publications

(9 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The existence of positive solutions of a BVP can be proved by constructing an associated operator and finding the fixed point of the operator. This idea has been widely applied to BVPs of integer order (for example, [4,11,13,15,18,22,25,27,28,29,33,35]), as well as to the study of fractional BVPs ( [1,5,14,17,20,23,26,39,41,43]). The construction of the associated operators is a key step in this approach.…”

Section: Introductionmentioning

confidence: 99%

Uniqueness of positive solutions of fractional boundary value problems with non-homogeneous integral boundary conditions

Graef

Kong

et al. 2012

fcaa

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Uniqueness of positive solutions of fractional boundary value problems with non-homogeneous integral boundary conditions

Graef

Kong

et al. 2012

fcaa

Self Cite

View full text Add to dashboard Cite

show abstract

“…BVPs with two‐point or multi‐point nonlinear BCs have also been studied in the literature, for example, in 1, 2, 4, 5, 9, 11, 14. More specifically, Ehme et al 5 considered the BVP consisting of Eq.…”

Section: Introductionmentioning

confidence: 99%

Higher order multi-point boundary value problems

Graef

Kong

2010

Math. Nachr.

Self Cite

View full text Add to dashboard Cite

Key words Solutions, boundary value problems, lower and upper solutions, Nagumo condition, fixed point theorem MSC (2010) 34B15, 34B18We consider the boundary value problem u, u , . . . , u (n −1) = 0, t ∈ (0, 1),where n ≥ 2 and m ≥ 1 are integers, tj ∈ [0, 1] for j = 1, . . . , m, and f and gi , i = 0, . . . , n − 1, are continuous. We obtain sufficient conditions for the existence of a solution of the above problem based on the existence of lower and upper solutions. Explicit conditions are also found for the existence of a solution of the problem. The differential equation has dependence on all lower order derivatives of the unknown function, and the boundary conditions cover many multi-point boundary conditions studied in the literature. Schauder's fixed point theorem and appropriate Nagumo conditions are employed in the analysis. Examples are given to illustrate the results.

show abstract

“…For a small sample of such work, we refer the reader to [1], [2], [6], [7], [9], [10], [11], [12], [13], [14], [15] and the references therein. In particular, Graef, Henderson, and Yang [6] studied BVP (1.1), (1.2) with e(t) ≡ 0 on (0, 1), i.e., the BVP consisting of the equation…”

Section: Introductionmentioning

confidence: 99%