Positive solutions to second-order singular nonlocal problems: existence and sharp conditions

Autor: Shiqi Ma, Xuemei Zhang
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Zdroj: Boundary Value Problems, Vol 2019, Iss 1, Pp 1-18 (2019)
Druh dokumentu: article
ISSN: 1687-2770
DOI: 10.1186/s13661-019-1289-7
Popis: Abstract In this paper we consider sharp conditions on ω and f for the existence of C1[0,1] $C^{1}[0,1]$ positive solutions to a second-order singular nonlocal problem u″(t)+ω(t)f(t,u(t))=0 $u''(t)+\omega (t)f(t,u(t))=0$, u(0)=u(1)=∫01g(t)u(t)dt $u(0)=u(1)=\int _{0} ^{1}g(t)u(t)\,dt$; it turns out that this case is more difficult to handle than two point boundary value problems and needs some new ingredients in the arguments. On the technical level, we adopt the topological degree method.
Databáze: Directory of Open Access Journals
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