Premium
The mixed BVP for second order nonlinear ordinary differential equation at resonance
Author(s) -
Mukhigulashvili Sulkhan
Publication year - 2017
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.201500247
Subject(s) - mathematics , homogeneous , ordinary differential equation , order (exchange) , nonlinear system , homogeneous differential equation , mathematical analysis , resonance (particle physics) , differential equation , pure mathematics , combinatorics , differential algebraic equation , physics , finance , quantum mechanics , economics , particle physics
Efficient sufficient conditions are established for the solvability of the mixed problemu ′ ′( t ) = p ( t ) u ( t ) + f ( t , u ( t ) ) + h ( t ) ,u ( a ) = 0 ,u ′ ( b ) = 0 , where h , p ∈ L ( [ a , b ] ; R )andf ∈ K ( [ a , b ] × R ; R ) , in the case where the homogeneous linear problemw ′ ′( t ) = p ( t ) w ( t ) ,w ( a ) = 0 ,w ′ ( b ) = 0 has nontrivial solutions.