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Singular Dirichlet boundary value problems. II: Resonance case

Donal O'Regan (1998)

Czechoslovak Mathematical Journal

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 < .

Some global results for nonlinear fourth order eigenvalue problems

Ziyatkhan Aliyev (2014)

Open Mathematics

In this paper, we consider the nonlinear fourth order eigenvalue problem. We show the existence of family of unbounded continua of nontrivial solutions bifurcating from the line of trivial solutions. These global continua have properties similar to those found in Rabinowitz and Berestycki well-known global bifurcation theorems.

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