Premium
Second order problems with functional conditions including Sturm–Liouville and multipoint conditions
Author(s) -
Cabada Alberto,
O'Regan Donal,
Pouso Rodrigo L.
Publication year - 2008
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.200510675
Subject(s) - mathematics , cover (algebra) , order (exchange) , sturm–liouville theory , boundary value problem , type (biology) , boundary (topology) , pure mathematics , mathematical analysis , combinatorics , mechanical engineering , ecology , finance , engineering , economics , biology
In this paper we study the solvability of equations of the form ‐(d/d t ) φ ( t, u, u ( t ), u ′( t )) = f ( t, u, u ( t ), u ′( t )) for a.e. t ∈ I = [ a, b ], together with functional‐boundary conditions which cover, amongst others, Sturm–Liouville and multipoint boundary data as particular cases. Our approach uses upper and lower solutions together with growth restrictions of Nagumo's type. An example is presented to show the applicability of the obtained results. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)