Displaying similar documents to “Oscillatory solutions of singular equations arising in hydrodynamics.”

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.

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.

Comparison theorems for noncanonical third order nonlinear differential equations

Ivan Mojsej, Ján Ohriska (2007)

Open Mathematics

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The aim of our paper is to study oscillatory and asymptotic properties of solutions of nonlinear differential equations of the third order with quasiderivatives. We prove comparison theorems on property A between linear and nonlinear equations. Some integral criteria ensuring property A for nonlinear equations are also given. Our assumptions on the nonlinearity of f are restricted to its behavior only in a neighborhood of zero and a neighborhood of infinity.