On Green's functions and positive solutions for boundary value problems on time scales

By Ferhan Merdivenci Atici, Gusein Sh. Guseinov. 2002

334 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/ae9131fbf9561e861dfccfbd6b359931e73a560e

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In Applied Mathematics

In Modeling and Simulation

Citations in the corpus

Solutions to Second-order Three-point Problems on Time Scales (2002, background): “The following definitions, that can be found in Atici and Guseinov [4] and Bohner and Peterson [7], lay out the terms and notation needed later in the discussion.”
Singular second-order multipoint dynamic boundary value problems with mixed derivatives (2006, background): “For the main notions and facts from Lebesgue measures and Lebesgue integrals theory, we refer the reader to [5] and [7, pages 157–163].”
Double positive solutions of three-point boundary value problems for p-Laplacian dynamic equations on time scales (2005, background): “For convenience, we list the following well-known definitions which can be found in [1,5,9,16,18] .”
Existence theory for positive solutions to one-dimensional p-Laplacian boundary value problems on time scales (2007, background): “Recently, there is much attention paid to question of positive solutions of boundary value problems for second order dynamic equations on time scales, see [4–9,11,12,15–17,19–21,27, 32,35,36].”
Notes on the diamond-α dynamic derivative on time scales (2007, methodology): “To show the existence of the delta derivative does not imply the existence nabla derivative, we may consider the same function f at point 0 on a time scale T = [−1,0] ∪ [1,2].”
Existence results for singular three point boundary value problems on time scales (2004, methodology): “Various aspects of mixed problems hav investigated in the literature, such as Green’s functions [9,11], the existence of m positive solutions [5], and the quasilinearization method [10].”
Triple positive solutions of boundary value problems for p-Laplacian dynamic equations on time scales (2006, neutral): “For convenience, we list the following well-known definitions which can be found in [1,4,8, 9,15,16].”
Higher-order self-adjoint boundary-value problems on time scales (2006, methodology): “In [9], self-adjoint boundary-value problems (BVPs) for second-order dynamic equations on time scales were introduced and examined by making use of both delta and nabla derivatives.”
An application of time scales to economics (2006, methodology): “In this paper, the reader will find an economic application of the ∇-derivative and ∇-integral, first initiated by Atici and Guseinov [2].”