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Second order nonlocal boundary value problems at resonance
Author(s) -
Franco Daniel,
Infante Gennaro,
Zima Mirosława
Publication year - 2011
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200810841
Subject(s) - mathematics , boundary value problem , norm (philosophy) , order (exchange) , complement (music) , mathematical analysis , boundary (topology) , riemann–stieltjes integral , boundary values , resonance (particle physics) , integral equation , physics , law , finance , particle physics , biochemistry , chemistry , complementation , economics , gene , phenotype , political science
We present sufficient conditions for the existence of positive solutions for some second order boundary value problems at resonance. The boundary conditions that we study are quite general, involve a Stieltjes integral and include, as particular cases, multi‐point and integral boundary conditions. Our results are based on a Leggett‐Williams norm‐type theorem due to O'Regan and Zima. We employ a general abstract approach which allows us to improve and complement recent results in the literature. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim