The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Singular problems on the half-line”

Disconjugacy and disfocality criteria for second order singular half-linear differential equations

Ondřej Došlý, Alexander Lomtatidze (1999)

Annales Polonici Mathematici

Similarity:

We establish Vallée Poussin type disconjugacy and disfocality criteria for the half-linear second order differential equation u ' ' = p ( t ) | u | α | u ' | 1 - α s g n u + g ( t ) u ' , where α ∈ (0,1] and the functions p , g ∈ L l o c ( a , b ) are allowed to have singularities at the end points t = a, t = b of the interval under consideration.

On a two-point boundary value problem for second order singular equations

Alexander Lomtatidze, P. Torres (2003)

Czechoslovak Mathematical Journal

Similarity:

The problem on the existence of a positive in the interval ] a , b [ solution of the boundary value problem u ' ' = f ( t , u ) + g ( t , u ) u ' ; u ( a + ) = 0 , u ( b - ) = 0 is considered, where the functions f and g ] a , b [ × ] 0 , + ∞ [ → ℝ satisfy the local Carathéodory conditions. The possibility for the functions f and g to have singularities in the first argument (for t = a and t = b ) and in the phase variable (for u = 0 ) is not excluded. Sufficient and, in some cases, necessary and sufficient conditions for the solvability of that problem are established.