The mixed BVP for second order nonlinear ordinary differential equation at resonance | Zendy

Mukhigulashvili Sulkhan | Zendy

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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.

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