Displaying similar documents to “Criteria for disfocality and disconjugacy for third order differential equations.”

Singular Dirichlet boundary value problems. II: Resonance case

Donal O'Regan (1998)

Czechoslovak Mathematical Journal

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Existence results are established for the resonant problem y ' ' + λ m a y = f ( t , y ) a.e. on [ 0 , 1 ] with y satisfying Dirichlet boundary conditions. The problem is singular since f is a Carathéodory function, a ∈ L l o c 1 ( 0 , 1 ) with a > 0 a.e. on [ 0 , 1 ] and ∫ 0 1 x ( 1 - x ) a ( x ) d x < ∞ .

Differential equations at resonance

Donal O&#039;Regan (1995)

Commentationes Mathematicae Universitatis Carolinae

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New existence results are presented for the two point singular “resonant” boundary value problem 1 p ( p y ' ) ' + r y + λ m q y = f ( t , y , p y ' ) a.eȯn [ 0 , 1 ] with y satisfying Sturm Liouville or Periodic boundary conditions. Here λ m is the ( m + 1 ) s t eigenvalue of 1 p q [ ( p u ' ) ' + r p u ] + λ u = 0 a.eȯn [ 0 , 1 ] with u satisfying Sturm Liouville or Periodic boundary data.