Solvability of Hammerstein Integral Equations with Applications to Boundary Value Problems
Daria BugajewskaAdam Mickiewicz University, Poznan, Poland
Gennaro InfanteUniversita della Calabria, Cosenza, Italy
Piotr KasprzakAdam Mickiewicz University, Poznan, Poland
In this paper we present some new results regarding the solvability of nonlinear Hammerstein integral equations in a special cone of continuous functions. The proofs are based on a certain xed point theorem of Leggett and Williams type. We give an application of the abstract result to prove the existence of nontrivial solutions of a periodic boundary value problem. We also investigate, via a version of Krasnosel0ski's theorem for the sum of two operators, the solvability of perturbed Hammerstein integral equations in the space of continuous functions of bounded variation in the sense of Jordan. As an application of these results, we study the solvability of a boundary value problem subject to integral boundary conditions of Riemann–Stieltjes type. Some examples are presented in order to illustrate the obtained results.
Cite this article
Daria Bugajewska, Gennaro Infante, Piotr Kasprzak, Solvability of Hammerstein Integral Equations with Applications to Boundary Value Problems. Z. Anal. Anwend. 36 (2017), no. 4, pp. 393–417DOI 10.4171/ZAA/1594