Eigenvalue characterization for (n · p) boundary-value problems

Abstract

We consider the (n, p) boundary value problemwhere X > 0 and 0 < p < n -1 is fixed. We characterize the values of X such that the boundary value problem has a positive solution. For the special case X = 1, we also offer sufficient conditions for the existence of positive solutions of the boundary value problem.

Positive solutions and eigenvalues of conjugate boundary value problems

“…As for twin positive solutions, several studies on boundary value problems different from (E) can be found in [5,14,28,29,30]. Our results not only generalize and extend the known theorems for all the above eigenvalue problems, but also complement the work of many authors [3,15,16,24,33,35,36,38,39,40,41,42], as well as include several other known criteria offered in [1]. The outline of the paper is as follows.…”

Characterization of eigenvalues for difference Equations subject to Lidstone conditions

“…Further, problems related to continuous Lidstone boundary value problems have been the subject matter of many recent publications, e.g. see [2,4,29], and hundreds of references therein. We also note that while discrete boundary value problems such as conjugate type, focal type, Sturm-Liouville type, (n, p) type, have been discussed extensively in [1,2,4,8], the problem (L) is only briefly addressed in [1].…”

Existence and estimates of twin positive solution for two-point right focal boundary value problems

“…Their results have been generalized and extended in [2,35,38,40]. For related work, we refer to [4,[16][17][18]33,39,41].…”