Displaying similar documents to “On existence of proper solutions of quasilinear second order differential equations.”

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

Ondřej Došlý, Alexander Lomtatidze (1999)

Annales Polonici Mathematici

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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.

Singular problems on the half-line

Irena Rachůnková, Jan Tomeček (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The paper investigates singular nonlinear problems arising in hydrodynamics. In particular, it deals with the problem on the half-line of the form ( p ( t ) u ' ( t ) ) ' = p ( t ) f ( u ( t ) ) , u ' ( 0 ) = 0 , u ( ) = L . The existence of a strictly increasing solution (a homoclinic solution) of this problem is proved by the dynamical systems approach and the lower and upper functions method.