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Solvability of semilinear abstract equations at resonance
Author(s) -
Sinkala Zachariah
Publication year - 1994
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300007403
Subject(s) - mathematics , generalization , hilbert space , separable space , dimension (graph theory) , bounded operator , bounded function , operator (biology) , mathematical analysis , nonlinear system , kernel (algebra) , pure mathematics , reproducing kernel hilbert space , ordinary differential equation , space (punctuation) , differential operator , order (exchange) , differential equation , physics , biochemistry , chemistry , linguistics , philosophy , finance , repressor , quantum mechanics , transcription factor , economics , gene
We establish a generalization of the Cesari‐Kannan existence result for problems of the type Lx = N ( x ), x ∈ X where X is a separable Hilbert functional space, L is a selfadjoint linear differential operator with nontrivial finite dimensional kernel and N : X → X is a bounded continuous nonlinear operator. This generalization leads to new results when the dimension of the kernel of L is greater than one. Applications to systems of second order ordinary differential equations are given.