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Topological analysis of doubly nonlocal boundary value problems

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Abstract

We consider both Hammerstein integral equations and nonlocal boundary value problems in possession of two different nonlocal elements. The first occurs in the differential equation itself and takes the form \(\Vert u\Vert _q^q\). The second occurs in the boundary condition and takes the form of a Stieltjes integral. Because the nonlocal elements are not necessarily related, a careful analysis is required to control each nonlocal element simultaneously. Topological fixed point theory is used to deduce existence of at least one positive solution to the boundary value problem. And we illustrate the application of the results with an example.

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  1. School of Mathematics and Statistics, UNSW Sydney, Sydney, NSW, 2052, Australia

    Christopher S. Goodrich

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Correspondence to Christopher S. Goodrich.

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This paper is dedicated to the memory of Maddie Goodrich on the occasion of what would have been her 19th birthday.

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Goodrich, C.S. Topological analysis of doubly nonlocal boundary value problems. J. Fixed Point Theory Appl. 23, 29 (2021). https://doi.org/10.1007/s11784-021-00865-1

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