We consider semilinear boundary value problems of the form L u (x)= f (x, u (x))+ h (x),\quad
x ∈ (0, π),\tag*(1) where L is a 2m th-order, self-adjoint, disconjugate ordinary differential …

Half-eigenvalues of self-adjoint, 2mth order differential operators and semilinear problems with
jumping nonlinearities — Heriot-Watt Research Portal Skip to main navigation Skip to search …

Lu= au+− bu−+ λu+ h,(2) where u±(x)= max {±u (x), 0} for x∈[0, π], and λ is a real parameter.
Values of λ for which (2)(with h= 0) has a nontrivial solution u will be called half-eigenvalues …

In this paper we show that a sequence of half-eigenvalues exists, with certain properties,
and we prove various results regarding the existence and multiplicity of solutions of both (1) …