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- W4246793553 abstract "In this chapter we apply the results obtained in the previous ones in order to deduce existence of solutions of different nonlinear problems coupled with suitable boundary value conditions. We will point out the importance that the existence and constant sign of the related Green's function has in the deduction of such existence results. After an introductory section, we will show, in Section 4.2, several classical and recent results that ensure the existence of fixed points of operators defined in abstract spaces. The majority of them will be derived from the Leray–Schauder degree introduced in Subsection 4.2.1. Section 4.3 is concerned with the theory of lower and upper solutions. This is a very well-known technique that allows us to ensure the existence of solutions of the considered nonlinear problem by assuming the existence of a pair of functions that satisfy suitable inequalities. Section 4.4 is devoted to the study of monotone iterative techniques which, as in the case of the degree theory, are developed to general operators defined on abstract spaces and are applied to related nonlinear boundary value problems." @default.
- W4246793553 created "2022-05-12" @default.
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- W4246793553 date "2018-01-01" @default.
- W4246793553 modified "2023-09-23" @default.
- W4246793553 title "Nonlinear Equations" @default.
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- W4246793553 doi "https://doi.org/10.1016/b978-0-12-804117-8.00004-7" @default.
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