Positive Solutions of Nonlocal Boundary Value Problems: A Unified Approach

By J. R. L. Webb, Gennaro Infante. 2006

341 citations recorded by the source corpus.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d30ebf144cb20de022c08879f0631884e0a3e897

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In Applied Mathematics

In Numerical Analysis

Citations in the corpus

Non-negative solutions of systems of ODEs with coupled boundary conditions (2012, methodology): “We prove our results by means of the classical fixed point index theory (see for example the review of Amann [6] and the book of Guo and Lakshmikantham [13]) and also make use of ideas from the papers [16,17,32].”
Multiple nonnegative solutions of systems with coupled nonlinear boundary conditions (2013, methodology): “We utilize the following results of [43] regarding order preserving matrices: Definition 2.”
Solutions of perturbed Hammerstein integral equations with applications (2016, methodology): “We utilize the following results from [87] regarding order preserving matrices: Definition 3.”
Multiple positive solutions of singular fractional differential system involving Stieltjes integral conditions (2012, background): “For a comprehensive study of the case when there is a Stieltjes integral boundary condition at both ends, for the case of a differential equation of order two, see [24].”
Positive solutions for nonlinear nth-order singular eigenvalue problem with nonlocal conditions (2010, positive): “The papers [1–3] contain several new ideas, and give a unified approach to many BVPs.”
A CANTILEVER EQUATION WITH NONLINEAR BOUNDARY CONDITIONS (2009, background): “AMS (MOS) Subject Classifications: Primary 34B18, secondary 34B10, 47H10, 47H30”
Exact Iterative Solution for an Abstract Fractional Dynamic System Model for Bioprocess (2017, methodology): “For more details of the Riemann–Stieltjes integral conditions, we refer readers to the recent work of Webb and Infante [20–22].”
Positive solutions of a third order nonlocal boundary value problem (2007, background): “[5, 6], Graef and Yang [8, 9], Henderson and Wang [11], Karakostas and Tsamatos [12, 13], Nowakowski and Orpel [17], Wang [19], Webb [20], and Yang [21].”
ON POSITIVE SOLUTIONS TO NONLOCAL FRACTIONAL AND INTEGER-ORDER DIFFERENCE EQUATIONS (2011, methodology): “In particular, we have shown how the recent ideas of Infante and Webb [20] may be used to deduce the existence of at least one positive solution to problem (1.1)–(1.3) even when neither ψ nor φ is nonnegative for all y ≥ 0.”
A third order boundary value problem subject to nonlinear boundary conditions (2010, methodology): “The approach used in [14] relied on an extension of the results of [29], valid for equations of the type (1.”
On a discrete fractional three-point boundary value problem (2012, methodology): “An excellent reference for this programme of study can be found in a wonderful recent paper by Infante and Webb [ 23 ].”