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On Some Properties of the Dirichlet Problem at Resonance

  • Arnold Lepin
Published/Copyright: March 10, 2010
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Georgian Mathematical Journal
From the journal Volume 15 Issue 1

Abstract

The boundary value problem at resonance

π‘₯β€³ + π‘₯ = π‘ž sin 𝑑 + 𝑓(𝑑,π‘₯,π‘₯β€²), π‘₯(0) = 0, π‘₯(Ο€) = 0,

is considered, where 𝑓 : [0,Ο€] Γ— 𝑹2 β†’ 𝑹 is a bounded CarathΓ©odory function, π‘ž is a parameter. We state the multiplicity results without assuming that 𝑓 has limits.

Received: 2006-11-17
Published Online: 2010-03-10
Published in Print: 2008-March

Β© Heldermann Verlag

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