Higher-Order Functional Discontinuous Boundary Value Problems on the Half-Line

Feliz Minhós and Infeliz Coxe
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Feliz Minhós: Departamento de Matemática, Escola de Ciências e Tecnologia, Universidade de Évora, 7000-671 Évora, Portugal
Infeliz Coxe: Centro de Investigação em Matemática e Aplicações (CIMA), Instituto de Investigação e Formação Avançada, 7000-671 Évora, Portugal

Mathematics, 2021, vol. 9, issue 5, 1-16

Abstract: In this paper, we consider a discontinuous, fully nonlinear, higher-order equation on the half-line, together with functional boundary conditions, given by general continuous functions with dependence on the several derivatives and asymptotic information on the ( n ? 1 ) t h derivative of the unknown function. These functional conditions generalize the usual boundary data and allow other types of global assumptions on the unknown function and its derivatives, such as nonlocal, integro-differential, infinite multipoint, with maximum or minimum arguments, among others. Considering the half-line as the domain carries on a lack of compactness, which is overcome with the definition of a space of weighted functions and norms, and the equiconvergence at ? . In the last section, an example illustrates the applicability of our main result.

Keywords: functional higher-order problems; unbounded solutions; half-line; fixed-point theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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